A clay bar is in the form of a synthetic malleable material and a clay mitt is material that is on a towel to remove contaminants. A clay bar can remove heavier contaminants than a clay towel from the clear coat of the paint.
The downside of a clay bar is if you drop it you toss it. A clay towel can be dropped and re used after it is cleaned. A clay towel is best for maintenance decon of a vehicle. A clay bar is best for heavier contamination on a vehicle especially in the removal of paint over spray