The main types of air cannon

Handheld vortex blasters

This is the category most people mean. A moulded barrel, an elastic membrane at the back, and a handle. They are sized to be held and aimed in one hand, and typically reach five to seven metres.

Within this category the meaningful differences are barrel diameter, membrane tension and build quality. Everything else is styling.

Fog and smoke cannons

Mechanically identical to a handheld blaster, but paired with a fog source so the ring becomes visible. Used almost entirely for demonstration rather than play, since the fog needs replenishing and the setup is not portable.

DIY builds

A bucket with a hole cut in the base and a sheet of plastic stretched over the open end will produce vortex rings. It is a genuinely good demonstration project and costs almost nothing.

The limitations show up with use. Membrane tension is difficult to set consistently, the rim is rarely smooth enough to form a clean ring, and the whole thing is awkward to aim.

Industrial air cannons

Worth mentioning only so you can rule them out of a search. These are fixed installations using high-pressure compressed air to clear blockages in silos, hoppers and kilns. They share a name and nothing else.