It depends.
In
Tomcat, you originally dumped the war into the tomcat/webapps directory OR made an XML file in that directory that pointed to the location on the server's filesystem where a copy of the war resided. I believe that newer versions also allow you to upload the WAR from the Tomcat admin webapp.
In WebSphere, the preferred method is to use the WebSphere admin webapp to upload, but it's also permissible to copy the xAR directly into the WebSphere apps directory. I seem to recall WebLogic being setup the same.
The "ideal" method is to use JSR-88, which is a vendor-independent mechanism for allowing client programs to upload and install appserver components. AFAIK, that's still mostly experimental. I have been involved in the JSR-88 server subsystem for the JOnAS appserver.