What is the difference between lock and Mutex?

A lock is specific to the AppDomain, while Mutex to the Operating System allowing you to perform inter-process locking and synchronization (IPC).

lock is a compiler keyword, not an actual class or object. It's a wrapper around the functionality of the Monitor class and is designed to make the Monitor easier to work with for the common case.

The Monitor (and the lock keyword) are, as Darin said, restricted to the AppDomain. Primarily because a reference to a memory address (in the form of an instantiated object) is required to manage the "lock" and maintain the identity of the Monitor

The Mutex, on the other hand, is a .Net wrapper around an operating system construct, and can be used for system-wide synchronization, using string data (instead of a pointer to data) as its identifier. Two mutexes that reference two strings in two completely different memory addresses, but having the same data, will actually utilize the same operating-system mutex.