IBM Http Server is Apache Http Server plus some additional platform-specific directives. If you know Apache Http Server you know almost all there is to know about IBM Http Server. I know that on i5/OS (aka OS/400) there are several directives dealing specifically with OS/400 entities. Another subtlety about i5/OS is that the configuration file is stored in EBCDIC so you can't just edit it with a Ascii editor. I imagine on z/OS the situation is similar.
WebSphere Application Server is a J2EE- or JEE-compliant Java Application Server and is a completely different product. Think of it as a Java plugin for Apache Http Server equivalent to any other language plugin (CGI script, PHP, Ruby, Cobol, etc.). Http Server (Apache/IBM) doesn't understand how to run a Java program but the Application Server plugin does. Http Server passes the entire HTTP request to the plugin to process; Application Server processes the request and passes the HTTP response back to Http Server which in turn passes it to the TCP/IP stack for serializing back to the browser.