Terminology

Whereby definition is associated with terms, or distinctions are made between similar terms.

Q3
The Quake 3 engine as created by Id Software, Inc. This is the part of the program contained within the platform-specific binaries that (so far) are distributed without source text. Also known as "the EXE" in Windows.
Q3A
"Quake III: Arena", the first game created by Id Software designed to run on the Quake 3 engine. I make the distinction where "Q3" refers to the engine itself, and "Q3A" refers to the game(play). Mostly synonymous with "baseq3".
Q3TA
"Quake III: Team Arena", the second game created by Id Software designed to run on the Quake 3 engine. The source code to Q3TA is also packaged in baseq3, but (de)activated with compiler conditionals. Artwork (models, skins, maps, textures) are packaged separately (as a product) and for the most part is considered an entirely different product from Q3A.
baseq3
Refers primarily to the distributed source code for modifications on Q3, the source code corresponding to Q3A. Also used to refer to Q3A as a special case in the context of mods (the mod from which most others are derived, or "the original mod").