The main objective of functional testing is "to meet customer requirements". ( Developement and Testing of s/w project done as per customer requirements.)
Validation means validating the feature of that application.
Your question is like - There is a Big Circle and inside that there is Small circle. The area is the same when you consider together to cover.If we see differently, it is different.
Functional testing talks about whole part of the project or application.Validation talks about each and every feature of the application is valid or not as per end user requirement (validation testing).
Testing whole application as per user requirements.
testing independently different feature inside the application is validating.(accepting valid values, preventing invalid values)