BrenBarn parent
Yes, very strange that the phrase "possible moves" never occurs in the article. The key word is "possible". The article consistently just uses the phrasing "have moves" but this is not an obvious way of phrasing things to the average person (although I think it's more common in chess lingo).
in chess lingo the most common is “legal moves”
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)
"moves" includes the idea of possible. "reachable" chess positions can only be the result of moves which are only those possible, and any follow-on moves would also only be those that are possible