EAP:
A framework that allows you to implement whatever type of authentication you want. It is not a specific type of authentication in itself. E.g. LEAP is based
upon the EAP framework.
LEAP:
Still EAP, just uses a mutual password-based authentication mechanism and supports WEP key management (i.e. dynamic session keys). It is Cisco proprietary, requiring Cisco components (except for a few third parties). There are some downsides - it is only based upon user/passwords and uses the notoriously vulnerable MD4 based NT Lan Manager (NTLM) hashing (don't mention L0phtcrack in the same sentence as NTLM).