They are two different things, let me explain how each one works.
Bitcoin node is a program running o a server on the port 8332 and you can call that tool with RPC calls.
The server is the machine running Bitcoin Node, but since it's a server it could run other services in different ports like HTTP (80), SSH (22), NodeJS (3000), SMTP (25) and Bitcoin (8332).
When we talk about a bitcoin server, we are talking about a Server that is running Bitcoin Core (Node) and another programs Like SQL, Python or NodeJS... or others. So, when a user calls any action the flowchart looks something like this:
1.-User open the website or the app (Port 443)
2.-User request a withdraw (Site send the request to NodeJS for data verification on port 3000)
3.-NodeJS calls Bitcoin core with RPC on por (8332)
4.-Send the result data back to NodeJS and this print it in the Website.
If you where dealing direct with node, you only need to make the call and make the withdrawal without a third party interference.