In database cluster implementation we can have multiple ways to make sure how different nodes will communicate with each other.
Shared nothing approach: None of the nodes will use others memory or storage. This is best suited for the solutions where inter node communication is not required, i.e. a node can come up with a solution on its own.
Shared Memory: In this approach memory is shared, i.e. each node/ processor is working with same memory. This is used when we need nodes to share solutions/ calculations done by other nodes and are available in memory.
Shared Everything: In this approach nodes share memory plus storage. This makes sense when nodes are working on problem where calculations and data created/ used by node is dependent on others.