Wildfly version in JBoss EAP 7.1.0

JBoss EAP is the name for the Java EE application server that Red Hat produces and supports. The latest version is 6 at the moment and this implements Java EE 6.

JBoss AS/WildFly is the name for the community project that you can test. This community project will eventually become JBoss EAP. "WildFly" is just the new name for "AS", which stood for Application Server. Version numbering is a bit more difficult here. WildFly 8, WildFly 9, WildFly 10 and possibly additional WildFly versions are all milestones on the path to what eventually will be called JBoss EAP 7. They all implement Java EE 7.

Even though they're milestones on that path and not supported, some releases are actually quite stable and could be run into production (but since they're not supported this is at your own risk).

JBoss Web was the name of the Tomcat based Servlet container that Red Hat used in JBoss EAP 6 and earlier. From EAP 7 on (and thus already in WildFly 8,9,10) this will be replaced by a new Servlet container/http engine called Undertow.