WildFly is not shipped with the EAP. WildFly is a community project and JBoss EAP is a Red Hat product. They live in separate repositories and even if they usually have some common point in history, you can't say WildFly is shipped with EAP. The closest WildFly version to EAP 7.1 is WildFly 11.
To simplify creating layered projects/products, the core runtime of the application server was cut to a separate project - the WildFly core. It contains just a very basic functionality which allow to build projects on top of it (by adding modules and extensions). The core contains
- Modular class loading
- Unified management, including domain mode
- Basic deployment architecture
- CLI for management
Java 8 is supported for JBoss EAP 6.4. For details look into the EAP 6 supported configurations.