It is generally accepted that traditional Proto-Indo-European reconstructs late PIE to the exclusion of Anatolian (PS: not! see most recently Craig Melchert, "The Position of Anatolian"). We may call this PIE for simplicities sake. Some declare they mean core, proto-nuclear, etc. when saying PIE throughout.
The earlier stage respectively with Anatolian evidence taken into account may also be called PIE. Kloekhorst eg. uses the terminus Proto-Indo-Anatolian, formerly Proto-Indo-Hittite, because tree models of PIE branches generally agree that Anatolian branched off first, and because PIE is often used in the first definition.
The prefix pre- as in pre-PIE generally suggests an older, not savely determined of language. Pre-proto- is to be distinguished from a mere pre- that suggests unidentified substrates.
In sum, 1 and 2 are often conflated, but 3 is held strictly distinct. So far so good?
The pertinent question though, if we have to work strictly backwards in time, concerns what may be called a late Proto-Indo-European dialect continuum. The idea is known, but I don't think there was a substantial theory to take that name. Is it to be subsumed under "late PIE" or is it yet too early for this?