System testing is the final stage of testing before giving 
the project/product to client.

So system testing comprises of both functional testing and 
non-functional testing.

So as for the question, functional testing is part of a 
system testing

System testing is testing of the entire system as awhole. 
This is what the user see and feel abt the product you 
provide. 

System testing is actually done to the entire system 
against the Functional Requirement Specification(s) (FRS) 
and/or the System Requirement Specification (SRS). 
Moreover, the system testing is an investigatory testing 
phase, where the focus is to have almost a destructive 
attitude and test not only the design, but also the 
behaviour and even the believed expectations of the 
customer. It is also intended to test up to and beyond the 
bounds defined in the software/hardware requirements 
specification(s).

so functional testing is a part of system testing but they 
are not the same.

Functional testing is testing the required functionality in 
detail often following a document like a usecase for a 
module.
System testing is done when all the modules are integrated 
and the system needs to be tested as a whole.
Here the functional testing will be and end to end scenario.
e.g you have a change made in Module A you can see the 
change reflected in Module D.
Most often the system testing will invoke interfaces and 
adapters for the completion of a flow and hence is a more 
elobrate form of functional testing.

they are not same 
functional testing "testing the application whether it is 
working according to the customer requirement specification 
or not 

system testing:testing the overall fucnctionality of the 
application  is working correctly or not

Function testing- testing the  functionality of an 
application.
System testing- It's called end to end testing. While doing 
end to end testing, testing environment should be similar 
to the production environment. so testing the application 
in the environment which is similar to the production 
environment is called system tesing. we will test only end 
to end flow. so we are not going to test the functionality 
here. so functional testing and system testing both are 
different