I’d add that the detective is someone very much a part of the community, knows the people and deals with them regularly, and so can make assumptions about their behavior.
Therefore the Miss Marple books are cozies while the Hercule Poirot books are not. You can plop Poirot down anywhere, even in the Orient Express among total strangers. That makes him a detective rather than an ordinary person who stumbles across crimes in their small world.
I deliberately held off from reading Maserschmidt’s link until after I posted, but I see that makes the same point.
That page also says, rightly, that most cozies star women. The only major cozy series starring a man I can think of offhand are the Charles Paris mysteries by Simon Brett, whose “village” is the world of British entertainment.