The Wikipedia article goes on to say that other authors describe the second type as a "squeeze" -- I think Kemp uses that term -- and only the mutual or reciprocal kind as a true "zugzwang". I can't remember if it was GM Edmar Mednis or IM Rafael Klovsky who told me many years ago that it's only the mutual scenario that qualifies as a "true" zugzwang, but I'm pretty sure it was one or both of them. Either way, the subject has divided chess authors almost since inception of the term in the first place. You can see the Wikipedia article on Immortal Zugzwang, for instance, which is one of the earliest famous examples of "zugzwang" and is featured in Nimzovitch's classic treatise "My System", and at the same time, many other famous players like IM Andy Soltis and others disagreed with the use of the term for that game.

A great article with some really beautiful examples of zugzwang is: https://www.chesshistory.com/winter/extra/zugzwang.html. There's a very nice discussion at the end as well of a disagreement along just these lines as to what truly constitutes zugzwang, between Hooper and Myers.