"Play a C, sound your key," is the saying.
More accurately... "Play a (written) C (on that instrument), sounds its key," I say.
If that helps.
Everything a Bb clarinet reads will be written a whole step higher than concert pitch.
If you're on piano (C instrument), you'd have to write that a whole step higher for Bb clarinet. (like everyone says here) Or, if you have a Bb clarinet part, you'd have to play/read that down a whole step on piano (C instrument) if you want the actual pitch.