However, the former can also be misunderstood as talking about the general congruence relation (i.e. a relation $R$ such that $aRb$ and $cRd$ imply $(a\circ c)R(b\circ d)$ with respect to some binary operation $\circ$).
As Willie Wong points out in the comments, there's also the "congruence" of triangles from Euclidean geometry.
Therefore, in the interest of descriptive tagging, I propose to:
- Retag those questions in congruences which are about modular equations with modular-arithmetic. A synonym for modular-arithmetic mentioning "congruence" would be needed -- avoiding the current pitfall;
- Retag the ones about congruence relations with congruence-relations (if they exist -- I didn't check);
- Retag the ones about triangles with euclidean-geometry and/or a new tag, e.g. geometric-congruence;
- Perhaps blacklist congruences.