From my point of view, system testing is broadly classified 
into functional and non-func. testing. hence Functional 
Testing is a part of System Testing. 

In system testing, testers test the product typically like 
the end-user.Every single Interface,module and even minute 
details have to be tested in this System Testing.

Functional Testing aims at testing the various 
functionalities of the product being tested.These 
functionalities include load,volume,stress, 
scalability,security,performance,etc.

in functional testing we concentrate only about particular 
functionality in the application,with out bothering hw it 
works.
but in system testing we concentrate on role of the 
functionalityin whole application

In functional testing we actually ensure that the 
features/subsystem under test should behave as per the 
users requirements irrespective of knowing how internally 
it works and how it interacts with other entity.

 In sytem testing we test both functionality/non 
functionality of whole applications taking systems as a 
whole which also ensures the expected behaviour w.r.t 
user's requirements.

in functional testing we are concerned with main
functionality of the software rather then it cosmetic
problem as it is under development

in system testing very thing is done as by user requirement
now we are confirming and checking every functional and
non-fuctional requirements

for further info 

www.s-qa.blogspot.com