My toilet upstair started to stink -sewage smell. I trouble shot it by wrapping the toilet with ceram plastic wrap to pinpoint the problem. Once it was wrapped there was no more smell. I thought that it might be the wax ring but 1 day later the toilet downstairs starts to smell the same way. Before wrapping the top toilet, the 1st floor toilet did not smell. Could it be the vent???

Could it be the vent??? Unless you've noticed a lowering of the bowl level , (did you?) I don't think it's a venting problem. By wrapping the bowl you've eliminated the wax ring. Great job of pinpointing the smell. OK! If it isn't the wax seal and it isn't a low bowl level there's only one thing left. Here's what I think is happening,.
You flush or drain and the discharge goes down the drain pipe and hits a partial blockage and bounces back sending a bubble of sewer gas ahead of it. That's what you smell,.
The solution would be to pull the downstairs toilet and snake from there. If that took care of the downstairs toilet but you still haven odor from the upstairs one you might as well snake that one also. Good luck, Tom