To achieve high performance, the multi-processor and multi-computer architectures have evolved. With the multi-processor architecture, multiple processors share a common memory and communicate with each other by reading/writing to the shared memory. With multi-computers, multiple computers that don't share a single physical memory communicate with each other by passing messages. Distributed Shared Memory (DSM) deals with sharing memory in a physical, non-shared (distributed) architecture.
Let's look at each one and talk about their differences.