This may sound stupid but when someone is talking about the sharepoint server are they talking about the application server or does it mean everything so the application and the database server.
That kind of depends on the nature of your deployment. In a big enough environment, when someone says "SharePoint", they're probably referring to a farm of servers that include web front ends, application servers, workflow manager servers, etc.
If the environment is small enough, though, it can all exist on on piece of hardware. In that case, "SharePoint Server" probably means the box and all associated services running on the box that make SharePoint do SharePoint.
SharePoint Farm is consist of the Application servers as well as Database Server.
It is depend upon the topology you used in your farm, i.e WebFront End, Application server and Database Server.
In single server farm you can have all these on one server.
In multi server environment you have SharePoint on separate serves and Database server.
You can check the all servers in the SharePoint farm from Central admin > System Settings > manage server in this farm. You will know about all SharePoint and DB servers.
Now, for SharePoint patch, it only apply on the SharePoint servers. You need to install the patch and then run the config wizard on all SharePoint server. Except the Database Server if it is on dedicated server.