The public link below gives an overview of the four installation type options for the 11gR2 client:
Instant Client: Enables you to install only the shared libraries required by Oracle Call Interface (OCI), Oracle C++ Call Interface (OCCI), Pro*C, or Java database connectivity (JDBC) OCI applications. This installation type requires much less disk space than the other Oracle Client installation types.
Administrator: Enables applications to connect to an Oracle Database instance on the local system or on a remote system. It also provides tools that enable you to administer Oracle Database.
Runtime: Enables applications to connect to an Oracle Database instance on the local system or on a remote system.
Custom: Enables you to select individual components from the list of Administrator and Runtime components.
A complete list of which individual components are installed by which Installation Type can be found on My Oracle Support, Doc ID [1397346.1]. It also includes the different components that are installed only on Microsoft Windows and not on other platforms.
Because My Oracle Support requires an Oracle account to login and access this information, I do not believe it is allowed to be posted on public forums. However, if you already have a support account with Oracle, you can go to https://support.oracle.com to login and search for the Document ID posted above to reference the complete list of components included in each Installation Type as you requested.
EDIT: Also, to answer your second question, yes, "Oracle Data Provider for .NET" is the ODP.NET component.