notation - Why do we use "congruent to" instead of equal to?

I'm more familiar with the notation $a \equiv b \pmod c$, but I think this is equivalent to $a \bmod c = b \bmod c$, which makes it clear that we should put a $=$ instead of $\equiv$.

What's the reason for the change of sign? If it's to emphasize that modular equivalence is a congruence relation, why don't we use the $\equiv$ sign in both notations?