I just can't understand what is the difference between 'Arbitrary Waveform generator' and 'Synthesized Function generator'? Some basic points would be quite useful...
Arbitrary usually implies you get to specify the waveform using something like a Piece-wise table of voltage vs. time. FG usually implies it has a precanned set of functions, sine, trapazoid, triangle, square, pulse, etc.
An AFG often has the built-in waveforms of a FG plus can do arbitrary waveforms using a programmed piece-wise look-up table. Thus such an AFG can perform both types of tasks.