Is bitcoin node and bitcoin client the same thing? What is the difference between btc node and btc client?

Which one is bitcoin-core and which bitcoind?
The Bitcoin system runs on a peer-to-peer network.
Each device participating on this network is called a "node" (of the network).
This node is actually a device running a Bitcoin client program.
Technically speaking node and client coincide. However they are different concepts in my opinion. One refers to the role of being part of the network, while the other refers to having a Bitcoin client program running.

Bitcoin-Core is a client program; namely, the reference implementation.
Bitcoind is just the "daemon" of Bitcoin-Core, that is the client core, running in the background, and can be controlled by bitcoin-cli (the command-line interface) via RPC.