What determines whether Schengen flights have passport control?

In Europe, before the existence of the Schengen area, national terminals were used only for internal flights and had no control desks. Then they started moving flights from the international terminals to the national ones because the disembarking procedures were faster and the Schengen agreements made the controls redundant. But then many Airports moved all the European flights to the local terminals and not all the European countries belong to the Schengen area. So things became confusing depending on the choices of the airport administration, that is why it is something that happens randomly.

You are confusing two entirely different types of passport control.

When you arrive in a Schengen country from outside the Schengen area, you go through immigrations. This is your UK to Amsterdam case. This is where passports, visas and other papers are checked and where you could be denied entry into the country.

There are also non-immigration passport controls. This could be the police searching for someone specific, it could be the airline checking (e.g. that you are the person who bought the ticket, or because they decided that today they're enforcing the part of their conditions of carriage that say you must have a valid passport), or it could be just random for whatever reason. The most common (by my experience) is that the airline asks for passports when boarding. I have no idea what the consequences would be by law if you refuse to or are unable to provide ID at this point, in the worst case they can probably deny you boarding the plane. There's the small but important difference - you are not refused entry into a country by a government authority, but refused transport by a private entity. The first can damage your future chances for a visa.

These second checks seem to be entirely random. I have done regular business trips between the same airports, to the point of having the exact same flight on the same weekday and time, and sometimes they asked for passports and other times not. Many of these flights were point-to-point from the Schengen area of the airport, so it can't be that some other passenger came in from some out-of-Schengen origin - he would've gone through immigrations long before arriving at the boarding gate.

There are some flights which stop twice in the Schengen area - one example of this is a Scoot flight from Singapore to Athens and then on to Berlin, which also takes passengers between Athens and Berlin. In this case, although passengers flying from Athens to Berlin are making an intra-Schengen flight, they must pass through passport control at Berlin airport as there would otherwise be no way for the authorities to separate those passengers arriving from Singapore from those arriving from Athens.

Saying that, I (along with all passengers) have also in the past had to go through passport control in Berlin from a direct easyJet flight which originated in Athens, however my guess is that this was done as part of the suspension of passportless travel due to the pressure on Schengen's southern borders during the migration crisis a few years ago.

In general, there should be no passport control for flights within the Schengen area. (Officers can stop you informally and ask to see your passport, but you will not pass through the formal control point and you will not receive a stamp.)

When you arrive at a Schengen airport from outside the Schengen area, you normally have passport control unless your departing flight is going outside the Schengen area.

Usually when I do this same flight I'm coming via another flight from the UK and there is security before the 1st and after the 2nd flight.

Security aside, the immigration controls in this case should be in Amsterdam only, where you go through the entry checkpoint on arrival regardless of whether you leave for Geneva immediately or days later. In the opposite direction, you would encounter the exit checkpoint in Amsterdam and an entry check at your UK destination.

Usually when i fly between schengen countries I hit passport control -I guess this comes about because though I may be going between schengen countries, very often its not a direct flight and many of those changing onto my second flight come from outside schengen.

This is a bit puzzling. The way this works at most major Schengen airports, including Schiphol, is that part of the airport is "in" and part of the airport is "out" of the Schengen area -- international. Flights arrive in one part of the airport or the other depending on where they're coming from. To transfer to a flight in the other part of the airport, a passenger has to go through the appropriate passport control checkpoint depending on the direction (in to out or vice versa).

If you fly from London to Geneva via Amsterdam, your first flight deposits you in the non-Schengen part of the airport and your second flight leaves from the Schengen part of the airport. You have to go through passport control to get there. If some passengers on the second flight had come from Munich, they would have landed in the Schengen part of the airport, so they can get to the departure gate without going through passport control.

it's random. I'm unlucky in getting this most of the time.

If you're experiencing "informal" a.k.a. "non-systematic" controls, this is it. These will have been far more common during COVID-19 as well as during times of elevated fear of terrorism or concern about refugees.

it's based on the flights manifest and whether any single passenger is connecting from a non schengen country. That is if one guy is coming from a UK flight onto the Amsterdam to Geneva one then everyone has to get their passport checked in Geneva.

If your getting checked in Geneva is related to the manifest, it won't likely be because of passengers originating outside the Schengen area, since those will have been stamped into the Schengen area in Amsterdam, but rather because of more specific intelligence about some passenger being perhaps wanted by the police or perhaps traveling on a passport that raises some suspicion. I encountered some checks that seemed to be of this nature in Oslo years ago; the agents didn't even open the passports of most people when they saw from the cover which country had issued them. These agents came to the jet bridge to screen the arriving passengers.

Based on my (very biased but quite substantial) experience, the most common scenario is that the only ID check is at the gate when boarding. For all I know, it might simply be for the airline's own commercial purposes (making it more difficult to resell or give a non-changeable ticket to someone else). I have also taken flights within the Schengen area (Stuttgart-Amsterdam is one I remember) where I did not have to show my passport to anybody at any point. I just boarded with my (eletronic) boarding pass and that's it.

I have also occasionally had to go through a formal passport control (e.g. because my flight happened to depart from a non-Schengen part of the airport) or seen the police waiting at the door of the plane (e.g. looking for someone in particular). And if you are taking a Schengen-Schengen flight as part of a longer trip, you should expect the staff at the check-in desk in the first airport to check that you have the right to enter your final destination.