It's technically not a signal generator but an Arbitrary Waveform Generator. It provides a base-band modulated signal to the signal generator which the sig gen upconverts to the RF carrier. If you purchased a Vector Signal Generator this would be built in but you can still buy them stand alone and they are pretty common. NI, R&S, Tek, and Keysight all have product lines of them.
Another way to think about it, this would be comparable to a signal generator in the same way that an oscilloscope is comparable to a spectrum analyzer.
What you call a signal generator is what most would call an RF signal generator. Both an AWG and an RF signal generator belong to the generic signal generator family. :-)
Another way to think about it, this would be comparable to a signal generator in the same way that an oscilloscope is comparable to a spectrum analyzer.