That used to confuse me, too. Turned out that when they were introduced, a hunter's or angler's gear box or pack was his "kit." If he carried a gun in it, it was his "kit" gun.
I had a Model 34, but extraction was almost impossible. I had to literally pound the extractor rod with the heel of my hand or a mallet. I asked Roy Jinks about it, and he admitted that S&W .22 revolvers have had such problems for decades.
He suggested trying different ammo (I already had) and having the chambers polished. But I was too bummed with it, and sold the gun and a very nice Safariland basketweave holster. Yeah, I warned the new owner, who said he'd just have the factory polish the chambers if he had trouble.
One reason why I sold it was that I think a .22 revolver isn't enough gun for the outdoors. I now use either a M-60-4 .38 or a Ruger SP-101 .357 when I want a small, handy revolver for protection and small game hunting.
However,some people like the .22, and not all Kit Guns have the problem that mine did. But none should!