OIF is a federation product from Oracle which can act as both Identity Provider (IdP) or Service Provider (SP). More on Federation basics IdP/SP here
OAM is a web Single Sign-On product from Oracle and also comes with its own authentication engine and can be integrated with OID for authentication (For OAM 184.108.40.206 integration with OID click here and for OAM 220.127.116.11 integration with OID click here ).
OAM can be integrated with OIF in one of two mode
1. OAM acting as authentication Engine with OIF: In this OAM-OIF integration, unauthenticated users are redirected to OAM for authentication. OAM authenticates user against its configured LDAP server and creates session in both OAM and OIF. In this mode OIF delegates authentication to OAM and OAM acts as Authentication Provider. To configure this type of integration follow steps here or here
2. OIF acting as authentication Engine (IdP) with OAM: In this integration, unauthenticated users are redirected to Identity Provider of OIF for authentication. OIF (acting as IdP) authenticates user against its configured authentication engine and creates session in both OIF and OAM. In this mode OIF acts as Identity Provider for OAM. To configure this type of integration follow steps here or here
Note : In this type of OAM-OIF integration where OIF acts as authentication engine for OAM, steps are slightly different between OIF 18.104.22.168 and OIF 22.214.171.124 (OIF 126.96.36.199 uses OAM 11g SP Module where as OIF 188.8.131.52 uses OSSO SP Module)
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