'If P is true, Q is true; if P is false, Q is false.' The relation of these two propositions is

The two propositions have exactly the same truth value in every case, so they are equivalent.

When P is true Q is true, and when P is false Q is false.

Thus P and Q are true together and false together.

This means P holds if and only if Q holds.

Sharing truth value across all cases is logical equivalence.