Were/are the Gaels, Picts and Britons physically distinct?

no answer is correct. The assumption is that the Britons were one group, the Picts were one group and the Scots were group etc. However the entire opposite is true. In the 1st century AD Tactius pointed out at least 3 different origins for the natives of Britons - Germanic, Gaul and Iberian (Spain). Within the so -called "Pictish North East" there are welsh placenames beginning with Aber near Gaelic placenames beginning with Inver, but Aber and Inver have the same meaning, so 2 grousp of people in "Pictavia" speaking 2 different languages. In the 4th century AD Marcellinus identified that the Picts were 2 distinct groups - the Verturiones and the Dicalydones- given that they were made up of many different tribes then this indicates that these 2 groups are of different characteristics.

Britain has no real indigenous population - settlement began over 5000 years ago, and multiple groups from various backgrounds settled here. As to the Britons of Scotland - Traditionally Strathclyde in the south west of Scotland was seen as a Brythonic kingdom, however the ONLY archaeological evidence of settlement from Ireland occurs in the Southwest of Scotland between the 6th century BC and 1st century AD, with the finding of axe heads and the building of irish style Crannogs occurring right up to Perthshire. There is absolutely no evidence of settlement from Ireland in the 5th/6th century post roman period. So in the dark ages the "Welsh Strathclyde" was actually populated by a people of Irish origin - causing one of the biggest mysteries of all time....why are Irishmen speaking "welsh".

So supposed "Britons" were Irish, another group Iberian, another group from Gaul. The Gauls themselves mentioned to Marcellinus in the 4th century AD that part of their population was indigenous but had been joined by other groups from "north of the Rhine", so there had been a population movement occurring in Europe - Britain was unlikely to have been missed out by this incoming population, and given that "North of the Rhine" lies Scandinavia which is also directly opposite the North East of Scotland, then it is a realistic expectation that they would have also landed in prehistoric Scotland.

Also the numbers are entirely against it - population grew exponentially at a rate of approx. 1.6x every 1000 years in this period - the population of Scotland was at least 200,000, and this may be a very, very conservative estimate, and the Picts traditionally were supposedly the vast majority of the population - maybe 17 out of 18 tribes. It would have been impossible for them to have reached this number as an indigenous people. The "traditional" symbolism of Picts - the symbol stones only commence in the 4th century AD, about 100 years after the Scandinavians started created their Stone runic monuments and 400 years after the Romans first landed in Britain.

The Picts were not indigenous, nor were the Britons and neither were the Scots or the Anglo-Saxons. These were all "mongrel" groups of people. Personally I like the Bede and Nennius argument - the Britons arrived first, then the Picts, then the Scots and the Romans last of all. Bede's argument that the Picts had "wives of the Irish" has a semblance of fact - the Picts mixed and married with other groups, and themselves were not a single heterogeneous population, with probably native, Scandinavian, Brythonic and Irish mixed ancestry - if you look close enough and localise your "search" to only a very small area or characteristic", you will find evidence of an" indigenous" population, but that does not prove that that indigenous population called themselves or knew themselves as Picts - so what you end up is what we have now - we have theories supporting Gaelic Picts, Scandinavian Picts, Brythonic Picts and Indigenous Picts. they are all correct and they are all wrong. It was a coalition of a mixed bag of people under a loose term of Pict, and the term can only be dated to c. 297AD in a poem by Eumennius in praise of the Emperor Constantius Chlorus - some 5297 years after the first settlers started to arrive in Britain.

There is more detail on this in "The Evolution of the Picts" and the "History of the Scots, Picts and Britons" on Amazon

Note: I read the question this morning, then wrote my answer tonight. Somehow I came to think it included language and culture. It's now a bit of TMI, but I'm going to let it hang out there for a little bit because I worked on it for a few hours (sigh).

Their is some controversy surrounding the relation of Brittonic and Gaelic people. One theory says that they were both indigenous to islands, while the other says that Brittonic speakers came after 450 B.C. The Celtic language was originally discovered by Edward Lhuyd. He discerned a similarity in the two surviving Celtic languages, Gaelic (Irish) and Brittonic (Welsh). He became the first to propose that these were ancient languages that were spoken throughout Europe. He classified two families, of which Brittonic and Gaelic were the main members, into P-celtic and Q-celtic. He further proposed a Proto-Celtic substratum (not to be confused with P-Celtic). P-Celtic languages were also known as Gallo-Brittonic because they originated in Northern Gaul. They are also called Continental Celtic because they were mostly spoken on the continent. Q-Celtic has a more western, coastal distribution. It includes Goidelic (Irish-Gaelic), and Celtiberian (parts of Iberia). P Celtic is a younger, innovative branch of Celtic. Q Celtic represents and older, conservative culture, possibly dating from the Bronze or early Iron Age. This theory has taken the back seat in the last few decades, but has adherents.

The implication of this theory is that Brittonic people are related to Continental Celtic speakers, especially across the channel in Northwestern Gaul. There is evidence to support this. One point is the similar names of tribes on either side of the channel. I think that it had to do with the spread of La Tene culture into Britain. One theory says that they only entered the island in a significant numbers after 200 B.C. They also introduced coinage to the island from the continent c. 150 B.C. They pushed the previous Goidelic speakers out of Southern Britain.

In the 1970's a new theory emerged. This put Goidelic and Brittonic in a new category called Insular Celtic. It says that Brittonic and Goidelic developed together on the islands, and separated from each other at some point. The term Insular describes their isolation from Continental Celtic. Continental, therefore, would not be related to Brittonic, and would be completely extinct. The implication of this is that the both language groups are indigenous from a much earlier date, like the early Iron Age. The Insular Celtic theory has become the mainstream viewpoint, but their are proponents of the Gallo-Brittonic connection.

Goidelic is in fact related to the Celtiberian languages. This supports the older theory. It is also intriguing from the standpoint of Irish Legend. Irish Legends were compiled in the 12th century. In them, the eponymous ancestor of the Irish people was an Egyptian princess named Scota. She married a Babylonian and their son was Goidel Glas, the originator of the Goidelic languages. It describes the adventure his group of people who are called Milesians. They came from Asia, stopped in Iberia, then arrived in Ireland.

Ancient Irish people during the Roman period were called Scotti. Ireland was called Scotta. In a semi legendary reconstruction, they were the ancestors of the Scots. The Scotti created a kingdom called Dal Riata in the Western Scottish Isles, during the sixth century A.D. It contested with other people like the Angles and Vikings over the next centuries. Dal Riata imparted the Gaelic language and customs onto the Picts (who were a more savage people). It merged with them to create the Kingdom of Alba, c. 900. This was the predecessor to Medieval Scotland, which was a combination of this and Norman settlers.

Picts were described as foreigners by many people. They were often called Huns or Scythians. Their name is derived from the custom of painting their faces. They formed a confederacy in the far north of Britain during the Romano British period. I think they may have previously been the enemies of Brittonic people. They originally spoke a distinct language called Pictish. They had a distinct form of art that was a fusion of of La Tene with later influences. They were viewed as the most archaic people of Britain, and this probably wasn't a maligned observation. Nobody knows where they came from.

What I haven't mentioned yet are the Brittonic speakers, which do not deserve to be last. Brittonic speakers were the primary subjects of Roman Britain, thus the name. After the Anglo Saxon invasions, the Brittonic speakers were represented by the Welsh, Cornish ("West Welsh"), and the Bretons. Cornwall was conquered by the Saxons at some point in the 10th century, and were assimilated. (Cornish identity was revived in the 20th century.) Wales was divided into a number of kingdoms which fought with eachother. The longest lasting one was the mountainous Kingdom of Gwynedd The Welsh seem to have held on to a remnant of Roman culture for a few centuries. They were a fiercely independent. They introduced the longbow to the English. They were eventually conquered in the 13th century, but most kept their identity and language.

Bretons were incorporated into France (Brittany) in the 15th century.

This area has evolved much in the past few decades of research. You are asking 'ethnicity' not race (there are only 3, possibly 4, 'races' of humans on the world. I should include as an edit that this is considered an outdated model). Ethnicity divides us into smaller groups from there. http://blog.world-mysteries.com/science/how-many-major-races-are-there-in-the-world/

To the question...a few studies have been done on the genetic history of England:

http://www.bbc.com/news/science-environment-31905764

The finding is the first genetic evidence to confirm what some archaeologists have long been arguing: that Celts represent a tradition or culture rather than a genetic or racial grouping.

The study was originally expecting to see a distinct Celt bloodline...but no:

"I had assumed at the very early stages of the project that there was going to be this uniform Celtic fringe extending from Cornwall through to Wales into Scotland. And this has very definitely not been the case," he told BBC News.

and

"People in South Wales are also quite different genetically to people in north Wales, who are both different in turn to the Scots. We did not find a single genetic group corresponding to the Celtic traditions in the western fringes of Britain."

So the answer is yes, Britons and Picts are genetically different from the Celts, though Celtic culture appeared to dominate their genetics did not. They still would have had many consistent features as far as appearance goes, but they are genetically distinct.

The study also notes that there are two genetic groupings in Northern Ireland: one of which also contains individuals across the sea in western Scotland and the Highlands; the other contains individuals in southern Scotland and southern England.

I believe the Northern Ireland genetics found in Scotland are Pictish bloodlines

It appears that 'Britons' is a pretty heavy simplification as well and represents 5 or 6 distinct genetic groupings:

Prof Mark Robinson, an archaeologist who works with Prof Donnelly at Oxford University, said he was "very surprised" that Celtic groups in Cornwall, Wales, Northern Ireland and Scotland had such different genetic patterns.

Editting:

I'm still trying to determine impact of this new discovery...but the Cheddar Man might give us different insights here... the Cheddar Man's DNA may make up close to 10% of a Briton's genes and that very well may make a distinct physiological difference. More to come.