I have seen three types of stake pool nodes mentioned.
- Active
- Relay
- Passive
How do they differ in purpose and function?
The term active node is often used to describe a node with the purpose of minting new blocks.
The term relay node is used to describe a node that is run by the stake pool operator to relay the newly minted blocks from their block producer (active node) to the rest of the Cardano network. See What are relay nodes?
A passive node is a node within the Cardano network that is receiving blocks and transactions from their peers (and in the future, will share these with its peers). A good example of an passive node is the Daedalus full node wallet.
Note that all type of nodes connected to the Cardano network can be used to submit a valid transaction to the network.