First, some definitions for the purposes of this answer. A node is an instance of a software which communicates with other nodes and validates and relays blocks and transactions. A wallet is an instance or subprocess of a software which allows a user to send and receive Bitcoin transactions.
By these definitions, not every wallet is a node. Wallets communicate with one or more nodes in order to send and receive transactions, however not every wallet acts as a node.
For example, consider a SPV wallet that runs on a phone (such as the Schildbach Android wallet). These wallets will connect to nodes on the Bitcoin network and use the Bitcoin P2P protocol. However they do not validate blocks and transactions, nor do they relay transactions to other nodes. They will ask the nodes that they connect to to filter specific blocks and transactions for them, and to forward it just those transactions. It does not do any validating nor does it do any relaying, so it is not considered a node.
