The SMPTE clock is read by the controller card of the Binloop (to start triggers) but not by the Reproducers. The reproducers use the V-sync clock to stay in sync after they start playing. If you are using only one Binloop, you don't need an external V-sync signal as it is generated internally. But if you have more than one Binloops, then you must use an external V-sync source to make sure that all the reproducers across multiple Binloops are working at the exact same speed.
Let me explain the different terms if it was a Dragon Boat Race.
Look at the video from the following link:
Each boat is a Binloop.
Each Rower(person) is a reproducer card.
The man beating the drum is V-Sync.
The yellow poles in front of the boats are the SMPTE triggers.
In the video you can see that the yellow poles in the water go down at the same time and all the boats start moving. This is just like when all the Binloops receive the trigger from SMPTE, all of the Binloops will start playback at the same time.
Once they start moving, all the rowers on each individual boat are going at the same speed (in sync) because the guy with the drum (V-sync) is telling them how fast or slow to row based on the beat fo the drum. It is the same way with the Binloops. The V-Sync is used to tell each reproducer card how fast to play.
If you notice, even though all the boats started at the same time, after a few seconds some go faster than the others.
This is because each boat is listening to their own drum guy in the front and they are going at their own individual speed (everyone in sync inside the boat but not across boats). But if all boats were to listen to only one drummer, all boats would move at the same speed in perfect sync. It is the same with the Binloops, they need the same external V-sync reference so that they stay in sync once they start going.
I hope this small comparison makes sense.