There are almost innumerable options when it comes to stock styles, for some rifles anyway. It'd be helpfull to have some idea of just what action/barrel combination we're considering.
Unfortunately, when it comes to .22RF rifles your off-the-shelf options for most manually-operated actions are pretty much limited to semi-custom models that will usually require some inletting and finish work or "factory replacement" styles where the original contours and dimensions are replicated.
While I obviously can't be familiar with the catalogs of all of the various outfits in the aftermarket, a quick look through the ones from Brownell's and Gun Parts Corp. pretty much cover what's commonly available.
There are loads of options for almost any centerfire action you can imagine, but unless you're buying for a Ruger 10/22 or Remington 597 semi-auto it looks as if custom or semi-custom is going to be your only option if you want somethiing different from OEM on a rimfire.
Be aware that in many cases this is going to cost you as much or more than a new, quality built rimfire rifle would. Almost certainly many times the cost of your average used rimfire of whatever action type, unless we're talking Dakota, Kimber, Winchester 52, or one of the other high-end specialized target rifle actions. Someone will make you anything you want for whatever you want, but cost-effectiveness is something only you can decide.
That said, nomenclature is more easily addressed in general terms: the name usually is descriptive of function. A "Varminter" style will contain design elements conducive to accomodating a medium-to-heavy contour barrel, a relatively wide, flat-ish bottomed forend, and geometry/dimensions best suited to aid shooting from a prone or rested position.
"American" could be descriptive of either the material used (I.E. "American" walnut) or what is more commonly referred to as the "classic" traditional layout favored by American shooters and found on most sporting rifles intended for the US market. Dimensions will vary slightly, but the overall lines and contours will be much the same. This is pretty much an "all-pupose" design compromise.
"Silhouette" stocks are designed to aid shooting from a standind, "off-hand" position, usually with a telescopic sight. The name comes from the game: Metallic Silhouette. Metal targets shaped and sized like game animals of different sizes are deployed in banks of five at ranges from 100 to 500 meters (for centerfires). In order to score as a "hit", the target must be knocked over.
FWIW, the stock that comes on almost any rimfire rifle is perfectly servicable for most general shooting purposes. It'd be a lot simpler and much less costly to modify what you've got in terms of length of pull, etc. to suit your build than to have one made. Just my $0.02. Your pocket depth and taste may vary.