The suicide specials (that's what they were actually called) are generally thought of as a class to themselves. There's at least one book on the subject.
I've not counted those in my numbers above.
Guns termed suicide specials are almost universally:
1. Spur trigger.
2. Very short barreled - 3" is long.
3. Chambered for rimfire cartridges, most commonly .22 Long or .32, but some were also available in .30, .38, and even .41 (I've never seen one chambered in .41).
4. Have a loading notch, but no loading gate.
5. Rarely have a maker's name.
6. Often have a "brand name" that might be shared among several makers.
Most makers were relative unknowns, but Iver Johnson, Forehand and Wadsworth, even Marlin made suicide specials.
Here's a great page that talks to makers and names used:
http://www.gun-data.com/suicide_specials.htm
My personal favorite brand name is Tramp's Terror. Just love the imagery that one suggests.
As far as I know, there are no figures for how many guns like these were produced, but some sources think the numbers were pretty massive, possibly in high hundreds of thousands, or more.
These truly were the bottom of the bottom for both price and quality, but most would fire a cartridge when the trigger was pulled.