I have been playing for nearly sixty years and have never been "confused" about the terminology used to describe the the pieces. Pawns refer to pawns, minor pieces refer to knights and bishops, and major pieces refer to the rooks and queens. Seems pretty clear to me.
A concept that needs a name
(1) You're wrong: "units" or "men" or "chessmen" are the terms for pieces and pawns collectively.
(2) I don't see that HMPs are a useful concept. I do see that distinguishing between kings and other pieces is a useful concept, though, since that issue arises in various contexts.
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(p. 152)
Man Any of the 32 chess units that constitute a chess set. A short-
ened version of the sexist term "chessman."
(p. 256)
Unit Any chess figure, whether a piece or a pawn.
Pandolfini, Bruce. 1995. Chess Thinking. New York: Simon & Schuster.
When we evaluate a position, we talk about material balance or material advantage. Some people distinguish between pieces and pawns while in fact all the things on the board are pieces. Confusion arises when sometimes we talk about the pieces other than the pawns. Should we call the pieces other than pawns and the king ( Rooks, Queen(s) , Knights and Bishops ) HIGH MOBILITY PIECES ( HMPs ) ?