Tube Patch or tubeless plug
A tubeles plug will not hold in a bicycles inner tube.

A tubeless plug is a short string of butyl rubber. About 1 cm in length and 2 mm wide. To fix a punctured tubeless tyre it is pushed with an awl into the hole. Together with sealant in the tyre it is good to seal cuts of up to 5 mm.

The inner tube's walls are too thin and too stretchy to seal it that way. The reasons are similar to those in my answer on sealants in inner tubes: https://bicycles.stackexchange.com/a/64642/30402

Fixing a clincher tyre that contains an inner tube with such a patch will not seal the puncture. Air would still escape through the valve hole, gaps in the rim, along the tyre bead, and countless other spots.

Fixing a small hole in clincher tyre when an inner tube still holds air is not necessary. The tyre itself doesn't need to be air tight. It just needs to hold the tube inside and provide a good contact patch to the ground. The plug cannot fix large holes in a tyre (check tyre boots). In such a case the threads of the carcass are ripped and the tyre loses the strength it requires to resist the pressure of the filled inner tube.