The only difference between the two is that the files in the zip file are in the jforum-2.1.8 subdirectory. The war is just a convenience package with everything (the WEB-INF directory in particular) in the root directory of the zip (as per war specs).
I don't use Oracle so I can't tell you the specifics. However, generally,
J2ee app containers have a deployment manager of some sort and in some cases an "autodeploy" feature. To use a war file, you will need to use one of these features. See your manuals for details.
Also, some app servers will only use the name of the war as the URL of the application. E.g., if the war deployed is named jforum-2.1.8.war, the url for this is /jforum-2.1.8. You might need to rename the war file to the URL you want to use, e.g. jforum.war or forums.war.
[originally posted on jforum.net by monroe]