I'm sometimes lucky enough to have a very gifted pianist, Annette, as an accompanist. If she's playing, I know I'll sound good. She has a degree in music, but she likes to have chords (plus the melody) for the songs she plays - she improvises amazingly on that platform, but she is one accomplished pianist who feels most most comfortable when she has the chords written out. If she doesn't have the chords, she works them out and writes them in.
I also sing with a classically-trained pianist who plays every note as written.

It's a whole hell of a lot more fun to sing when Annette is playing. If I make a mistake, she compensates. The other pianist plays exactly what's written, and isn't good at improvisation at all.

-Joe-