i think the most famous server is the WebSphere Application Server (WAS). The current version is 7. On a WAS you can run and deploy servlets, JSF-applications, EJB's and webservices. There are of course a lot of other application-types, but I would like to give you just a little picture of those types. Usually you install on a WAS multiple EAR-Files.
If you want to create portlets and to integrate those portlets in a portlet application you 'll also build one or more EAR-files. With a simple WAS your portlets a not able to interact with each other, so you need a WebSphere Portal Server (WP) which provides the implementation of both portlet specifications (JSR 168 and JSR 286). Behind the scenes you see that the WP is also just a WAS, but on the WAS is special Enterprise Application deployed, the WPS.ear. All the magic (e.g. Themes&Skins) what you 'll find in the WP comes from this WPS.ear application.
The last server is the WebSphere Process Server (WPS). If you want to build business processes with a tool like the WebSphere Integration Developer (WID) then the WPS 'll be your target runtime. Your business process 'll usually then use BPEL (or BPMN ?). I'm not sure how a WPS is constructed, but I would assume that you 'll there find also a WAS and an Enterprise Service Bus (ESB).