The .NET Framework Client Profile is a subset of the full .NET Framework. When you install the full framework you get the Client Profile plus some additional assemblies which complete the framework. So when say you have the Client Profile + Extended installed, you have the full framework installed.
Quoted from MSDN:
[The .NET Framework 4 Client Profile is] part of the .NET Framework. The .NET Framework is made up of the .NET Framework 4 Client Profile and .NET Framework 4 Extended components that exist separately in Programs and Features.