A functional test (FVT) test proves that a particular isolated function of a system works as designed. The function is given a particular input and the response from the system is checked against the 'known' good response. These tests will test what happens when incorrect data is used as input and input data that is on the edge of 'good' and 'bad'. I suppose the key phrase is that an FV test is quantitative. The input and ouput data can be described mainly because the function under test has been isolated from the rest of the system and is simple enough to be tested in this way.
System Testing (SVT) is often seen as being 'bigger better FV testing'. People often see SVT like this because a lot of effort has gone into developing the FV tests and running them again but harder and faster seems like an efficient use of an existing resource. However such a concept misses the real point. Customers do not use the functions of a system in isolation. You can see this in domestic application as well as large scale enterprise software. Take a word processor for example. A user does not use the save function in isolation. They use it alongside a document that; contains pictures, is in a different format, is actually stored on a network drive etc. thus just testing the function in isolation is not what your customer will do.
The real aim of SVT is to test the System as a whole in the way a customer will use it. This means using all useful combinations of the functions of a system to perform a particular task. When doing this we are looking to see if the system behaves in a 'reasonable' way. We can't use a specific input and expect a specific output as in a good system test there are just too many different options and circumstances for this to be a efficient method.