There is no difference in Functional Or Black Box 
Testing....because functional testing is the synonym of 
black box testing..

SYNONIMS :

White Box Testing : Open Box Testing,Clear Box      
Testing,Structural Testing,Glass Box Testing

Black Box Testing : Closed Box Testing,Behavioural 
Testing,Functinal Testing,Opaque Testing

But in the sense of System Testing...the definition of 
Functinal Testing is different...that is

In System Testing a Functinal Testing is the process of 
testing discrepancies of behaviour between Expected & 
Actual results.

Functional Testing: Behavior of the application according to
customer requirements or not.
Black box testing: testing the front end of the software
with out internal design(Coding).

Functional Testing is one of the testing types from the
Black Box Testing Methodology to test the application
functionality.