@Lord_Farin About your proposal. I am not sure whether it is better to keep (perhaps rename) congruences or to merge/synonimize this tag with modular-arithmetic.
That's why I have not upvoted your post. (At least not yet.)
But I certainly agree that it would be good to differentiate between several meanings of the word congruence used in mathematics.
@Lord_Farin I don't like the sound of the phrase modular congruence. (It sounds as a congruence with some additional property.) I would prefer congruence-number-theory.