Tyre pressure warning

The patch and plug is a patch that has a stem that is inserted into the hole. Your shop likely uses them while simply calling them patches.

Plugs are technically just for temporary repairs, which is why the shop won't do them. I have had them last years though, with only one failing to a slow leak.

 

They do take them off the rim however.
They insert the plug/patch from the inside? That would make sense.

 

Yes, though they would do the same for a plain patch for a hole in the tread. The patch & plug could leave something that looks like a plug on the outside if you want to check.

 

As @Trollbait explained, the only proper, permitted type of tire repair includes unmounting the tire from the rim and inspecting and patching from the inside with a patch and filling the hole with a plug. These days the patch and plug are usually combined into a single piece that is inserted from the inside.

Here are the instructions from Toyo Tires:

https://www.toyotires.com/media/5lujg1nb/tsd-12-018_proper_puncture_repair_guidelines_for_passenger_vehicle_and_light_truck_tiresf.pdf