Generally, a wallet is a piece of software that manages the user's key material, tracks their balance, and facilitates payments. On the Lightning Network, this means that a wallet must also be able to manage channels. These tasks could be handled by a thin client, under the assumption that it trusts a service provider for providing certain information.
Node software usually includes wallet capabilities but indicates further properties, such as being online at all times, participating in network gossip, and keeping track of the state of Bitcoin's blockchain by being directly to a co-hosted full node.