In B4J, when you create a non-UI App, it could be a Console, but not necessarily. Then personally you will call it Application (NON-UI). But that's my opinion.
It could be an http server, but there are several HTTP servers, with a graphical interface.
Console and server are not the same, but in some applications they can be the same and be both. But this is not necessarily the case.
Let me give some examples.
I can create a Non-UI App, passing a parameter turns me a WORD into PDF file. (eg. MyApp C: \ file.doc)
It is a console but it is not a server.
I can create a NON-UI app, which across the network sends a one second cadence, the exact time with UDP packets. It is a server but it is not a console.