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.

Further Reads:
https://www.quora.com/What-are-the-differences-between-shared-nothing-shared-memory-and-shared-storage-architectures-in-the-context-of-scalable-computing-analytics

https://en.wikipedia.org/wiki/Shared_nothing_architecture