In Tanach when discussing service of foreign gods the terms used are: elohim acheirim, el zar, el neichar. They all relate to the object of the service - the foreign gods. However in Chazal the usual term is avoda zara - foreign worship. Here we refer not to the object of the service but to the one who is serving. Not to the חפץ הנעבד but to the עובד. What is the reason for this change?
We find that a Jewish man can have the status of a goy. Either by serving idols or violating shabbos publicly or doing any aveira to get Hashem angry - להכעיס. Included is in this second category is one who is a kofer. The first way gives a person the status of a goy but NOT of a "min". The word "min" denotes a person who is in a category unto himself. The chidush is that a Jew can be considered a goy but not be in a category unto himself. The reason for this is that even one who violates shabbos has the opportunity to do tshuva and come back just as he left. He is thus not considered in his own distinct category. However one who is a kofer [the second category] IS considered a "min" because about him the pasuk says כל באיה לא ישובון - those who leave on the path of kfira cannot return [עי' ע"ז יז א ורמב"ם הל' ע"ז ב ה]. Not being able to return [in a conventional way] indeed classifies someone as a min - a separate, distinct category.
During the time of the נביאים there was a tremendous desire and lust to follow strange gods. One who did so was thus not considered a "min". He was just following his base desires, which while being forbidden, still would not make him a min. This was BEFORE the yetzer hara to serve idols had been eliminated. [The gemara in Chullin discusses the shchita of Achav as a shchitas mumar but not a shchitas min]. After the yetzer hara had been eliminated, in the period of the mishna and gemara , a person who served idols was considered a min. His act was much worse than it had been before. Without a yetzer hara to serve idols he nevertheless did so.
Now we understand why in the time of Chazal a new term came into usage - avoda zara - foreign service. We no longer relate to the idols [elohim acheirim, el zar, el neichar] but to the one performing the forbidden service. This is to show the severity of his act.
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