No, sync and quantization are different. Sync Source, Sync Unit, and Track Sync Unit apply only to the recording process. Their purpose is to create a loop with a size that matches the sync source, either a track, the host transport, or a MIDI clock.
Once you have the loop recorded, then quantization comes into play. Think of sync pulses as happening outside the track while quantization points happen inside the track. You have a little more flexibility with quantization because you can change the quantization points by adding more cycles through Multiply or Insert or adjusting the subcycles parameter to slice it up into smaller units.
Scheduling functions to happen on sync pulses rather than quantization points is a useful idea, we're starting to get there a little bit with the follower options in MIDI tracks. This will be part of a larger redesign of the quantization system. Besides more control over where quantization points are, there will be more control over which functions use quantization at all. The challenge is doing this in a way that doesn't result in configuration explosion, 4 quantization options multiplied by 50 functions. Suggestions are welcome.
You can of course do anything with scripts, but it would be nice if some of the most common quantization goals could be done without them.