Innovations in unified intra block copy (“BC”) and inter prediction modes are presented. In some example implementations, bitstream syntax, semantics of syntax elements and many coding/decoding processes for inter prediction mode are reused or slightly modified to enable intra BC prediction for blocks of a frame. For example, to provide intra BC prediction for a current block of a current picture, a motion compensation process applies a motion vector that indicates a displacement within the current picture, with the current picture being used as a reference picture for the motion compensation process. With this unification of syntax, semantics and coding/decoding processes, various coding/decoding tools designed for inter prediction mode, such as advanced motion vector prediction, merge mode and skip mode, can also be applied when intra BC prediction is used, which simplifies implementation of intra BC prediction.