But what correctly means? It means it has to be definitely a legal
position. So which are the illegal positions you should exclude? There
are the positions where one player is in check and it's not his move.
Also other countless types of illegal positions like:
8/8/5K2/8/2k5/1p6/1P6/B7 w - - that can't be reached with legal play.
Just because a position can't be reached from the initial position doesn't
mean that it isn't a position. It could be set as a problem, for example.
BUT also you have to define if you will handle the positions, taking
into account the "En Passant" rule, or the "50 Move Rule", or the "3
Move Repetition" rule, or the "Stalemate"(??) rule, or the "Castle"
rule or the player turn. And this is important.
The 50-move rule and three-fold repetition are irrelevant. Any position
that can be reached after repetitions can be reached without those
repetitions. Even taking this into account, these two rules only _allow_
the claim of a draw; they do not mandate it. Stalemate is irrelevant:
just because one of the players is stalemated in a position doesn't make
it any less of a position. Castling and en-passant are relevant: the FIDE
laws of chess define two positions as being different if they allow
different combinations of castling and en passant.
David Richerby Crystal Drink (TM): it's like a
refreshing juice beverage but it's