A lot of it iss the difference between being a musician and just being a player. A musician LISTENS to what other people are doing. A player just plays what they know.
A musician who accompanies usually doesn't play the melody, they fill in bits between, often during the gaps between what is sung. Most importantly, they watch the singer for clues that the singer is happy or otherwise with the accompaniment being added, its speed or appropriateness, and shut up if it isn't right.
Quack!
GtD.