All web servers are servers. Not all servers are web servers.

A server host services. A web server hosts a web service.

The server is the machine, from e.g dell, or a virtual machine subdividing a real piece of equipment

The webserver is a piece of software it runs that responds mostly to HTTP requests. e.g Apache, Nginx, Traefik, Caddy.

All webservers are running on a server. Not all servers run webserver software, they might be a fileserver running samba or nfs.

Both terms could refer to software or hardware, depending on the context.

I’d argue that web server generally refers to HTTP(S) servers more broadly regardless of whether they’re accessible on the web, a local network or even just the local interface.