What is the difference between Anatolia and Asia Minor?

The word, "Anatolia", was (and is still), a Greek word which referred (and still refers) to...."The East", that is to say, directly to the East of Greece proper, more specifically, what is today, the country of Turkey-(in its entirety and not simply based on a region or various regions). From the Greco-Aegean coast, to the borders with Armenia, Assyria, Kurdistan, Georgia and even Persia, the Ancient Greeks-(durnig pre-Roman times), referred to the starting point of Asia-(or West Asia), as "The East" or "Anatolia". The Ancient Greeks probably specified and identified each of the above mentioned individualized lands/countries-(it certainly was true regarding Persia proper); though more often, they simply identified this neighboring region as..."The East" or "Anatolia".

When the Romans conquered the lands of Anatolia-(including the Greco-Aegean region), they renamed Anatolia, to "Little Asia" or "Asia Minor". I don't remember which Roman Emperor officially changed the name from Anatolia to Asia Minor, nor do I have the exact or even approximate date of the name change-(regrettably). Roman Asia Minor included, the Greco-Aegean regions of Ionia, Lycia, Lydia and Phrygia, as well as the Greco-Anatolian interior lands of Cilicia, Pontus and Cappadocia. The lands of Armenia, Assyria, Kurdistan, Georgia and even the Northern periphery of Persia, all came under Roman colonial rule and subsequently, under its newly revised name....."Asia Minor".

In other words, there was never, nor is there, a geographical difference between Anatolia and Asia Minor....."it was one and the same". The only distinguishing difference was the name change which was invented by the Romans. Interestingly, the Byzantine and even the Modern Greeks continued (and continue) to use, "Asia Minor"-(conversationally), when referring to the various ethnically Hellenic lands within the Western and Central regions of PRE-Modern Turkey.

Although the answer is ticked as correct and helpful, it's completely wrong regarding naming origins. The name Asia was initially given by ancient Greeks to modern western Anatolia - later was used on about the same boundaries by the Romans for the roman province of Asia, which the Greeks called Asia or Asiane. The term Asia is of unidentified etymology. As mentioned correctly, the whole penisula was later called Asia Minor (Mikra Asia in Greek - Mikrasia is the term colloquially used in modern Greek, Mikrasiates the term for the Anatolian Greeks), in contrast to the rest of the continent which was named Asia.

The same name, Asia Minor, was used by medieval Greeks/Romans (medieval Greeks called themselves Romaioi, Romans in Greek. Byzantines is a neologism coined centuries after). One of the administrative-military provinces/divisions of the Eastern Roman empire (neologism, Byzantine Empire) was Eastern Division - Thema Anatolikon in Greek language. Thema Anatolikon covered the eastern part of Asia Minor, hence the name. From this term, Anatolikon, which appeared in medieval times, came the Latin deritive Anatolia. The greek term Anatolikon was also adopted by the invading turkic tribes as Anadolu, since they first invaded the Thema Anatolikon (Eastern Province/Division) of Roman Empire. Later it was used for the whole penisula.

Modern state of Turkey seems to extend the term to its whole Asian territory, not only the penisula. Probably it's a political decision, in order to avoid using geographic terms like Western Armenia, Northern/Upper Mesopotamia, Assyria, Kurdistan, inhabited in the past by Armenians, Assyrians/Syriacs and Kurds today.