They're talking about the trap. There are various designs, but yes the vent/overflow is a part of that which allows water to flow without creating a vacuum. It wouldn't make sense for it to be an issue if it only happens during showers.

Try running a shower with nobody in it. Does the shower head or the tub spout leak or spray some back onto the wall? If not, check the leak - it's probably dry. If it's dry, you need to check the seal around the vent/overflow, and around each handle and spout. You might need to tighten the screws a little on the vent, and caulk around it along the top half.

If the shower isn't spraying onto the wall with the handles, and you still see leaking, then you've got a leak somewhere between your tub spout and the shower head. Hopefully it's just the shower spigot in that case, because you can unscrew the entire thing, put some putty or Teflon tape on it, and screw it back in.

Another option would be to pour a bucket of water against that wall of the shower and see if that leaks. The biggest thing is just finding whether it's the plumbing leaking or the wall.