What is it when you can be singing in one key and then switch to different keys and keep the right notes to the tune, is this rare?

i have been told that this is perfect pitch, but after reading some of the answers given here, i’d have to say that it isn’t. one time i performed at an outdoor event where the piano had been stored in room connected to the outdoor stage, my pianist said it was out of key, but i had sang the song in key with the piano and had made the song turn out.
i also own a karaoke player (which changes keys) and can sing a song and change keys in the middle of it, keeping the melody line correct, sometimes without stopping, just sliding right into the new keys melody. and i do this sometimes 3–4 key changes in the same song. these are not key changes built into the song origionally.