These are definitions that I use, and I think its in agreement with what others use.
Open node: This implies that you have opened your RPC ports to the network, so that others can connect their wallets to it.
Remote node: This is how you would refer to an open node if you are the user of an open node. Alice runs an open node, and Bob connects to Alice’s open node so he is using a remote node.
Node: This is the standard Monero node. This means you are running the Monero daemon, the piece of software that connects to the other nodes on the network. Ideally, this software is being run on a computer where the incoming p2p port, 18080, is open, so that other nodes can connect to you.
Full node: This is somewhat semantics, but this implies that you are running a Monero node that is also solo-mining and also has the p2p ports open, so you are doing everything possible to contribute to the p2p decentralized network. This can also be called a mining node.
Monero Network Interface This is my preferred name for the monero node software. This definition is definitely not in agreement with what others think. But don’t you think its more descriptive?