Don't feel bad. The definitions of these terms are the same in at least a broad sense.
If you want to get more picky, a tone generator is the most specific term, denoting a device that creates tones for reference purposes, typically some very simple waveform like a pulse or a sine at a specific frequency (pitch). A synth module is a device that produces sounds when triggered by a MIDI signal. As well, the sounds are chosen and tailored by MIDI commands. A sound module- well that's pretty vague. When it comes right down to it, my cat is a sound module!
Hope that cleared it up.