in chess lingo, most common is "moves"; only in a weird circumstance (beginners?) would you need to say "legal".

the "possible" qualifier would probably be used for an "english" reason rather than a "chess" reason, to suggest "future" moves as opposed to the moves already made to get to a position. it would be more likely for whatever reason to say "how many possible moves" than "how many future/hypothetical moves", i.e. the use of possible is not to rule out the idea of impossible, simply to mean how many "could you make now from a particular position" and/or i guess to suggest "possible initial moves" as opposed to future follow-on moves.

the ambiguity is not really in chess, it's in english (and probably every other language also)

> the ambiguity is not really in chess, it's in english (and probably every other language also)

Sure, but the article is written in English. :-)