In a peer-to-peer architecture, all peers are supposed to be on the same level. There is no distinction between clients, servers, or other special roles.

Broker as integration function is a more central role in hub-and-spoke architectures. The broker typically maps and routes messages. The broker may be part of the central middleware or it can be attached as a separate component to a messaging system.

A grid architecture is a distributed set of nodes or systems which collaborate to serve a common goal. Typically, there is some central system which distributes sub-tasks and collects the results. The nodes may be computers or they may be parts of microchips. Look for “Systolic Arrays”.