Plugged bathroom sink, now unplugged. What the heck happened?

Factual Questions
1

I have 2 bathrooms, back to back. In bathroom 1, the sink was draining slow, so my SO used a plunger on it, improving the exit flow a bit. In the process, he managed to almost completely plug up the sink in bathroom 2. It took several hours for 3 cups of water to drain out of sink 2.

So, several runs of a Zip-it, to get all the hair out. An application of Drano (and letting it completely seep out, over several hours) followed by hot water. Then we used a small wet/dry vac to get that water out, and maybe loosen the clog, leaving us with a still clogged drain.

Stumped, and ready to call it a night, we dumped the water from the wet/dry vac into the adjacent toilet, flushed, and I watched the water left in the sink flow down the sink drain. The sink drain now empties just fine.

So what happened? Why did flushing the toilet (we had flushed it a couple of times within the hour before this) suddenly clean out my drain pipes in the sink?

2

I’m not a plumber, but my wife has long hair, so I’ve dealt with many a blocked drain! Best guess is that both the sink and toilet empty into the same pipe somewhere. The toilet water flowing past the sink outlet would have produced a small amount of suction in that pipe which would have pulled out the blockage from the sink that you had already loosened with the drano. The blockage was probably the other side of the trap so difficult to suck out from the sink side.