A signal generator generates either audio or RF frequencies (depending on the capabilities and designed purpose of the generator) for testing other electronics equipment. Makes it easier to make tests on a device without having to have it "in circuit". It's a lot easier to test a piece of equipment on a work bench rather than trying to test it in place.
A function generator supplies TTL (transistor to transistor) square wave pulses, sine and sawtooth wave forms for various testing purposes. It's a lot easier to work on something on the work bench and being able to remove a circuit board and just supply power and a signal saves having to take a whole piece of equipment into the shop. Then again, you also can use an oscilloscope for troubleshooting when you jave a good, known signal to work with. That applies to both types of generators.
Deb