I wonder if a move that checkmates is scored lower than a move that checkmates and captures.

Forced mates are generally scored with the number of moves to mate, e.g. "M2"

So you can start down a sequence that gives check-mate, but once it is the shortest sequence to check-mate, you have to abandon the check-mate.

So you can never actually play a mate in one.

Checkmate .. with advantage!