There are many practical issues associated with monitors that are not dealt with in the textbook descriptions - these issues are described in this paper. Stated without proof that monitors and message passing are equivalently powerful.
Monitor consists of entry procedures, internal procedures, and external procedures.
The monitor lock is not cleared when an external procedure is called. Two processes do wait, each expects signal from other. The awakened process then knows that notify just occured - more information than just that invariant established. Can be race conditions. M. p1 enters M, prempted by p2.