Okay, let’s back it up a notch, there’s something being slung off the fanblades here somewhere… 
Original question: Yes, they made 4-bore and 8-bore… and 10-bore, and 2-bore and yadda yadda. BUT… not every maker had the same concept of “bore”. It was somewhat like the original designation of “caliber”, in that the caliber was the length of the barrel in bores. (Using that terminology, the big 16"-bore Iowa-class battleship rifles are technically “fifty caliber” guns.)
Some used 12-bore, but that wasn’t the same as another maker’s “12-guage”. Still another maker might have called theirs an 8-guage but it might have had the same actual bore diameter as a fourth maker’s 10 guage.
That having been said, most of them are long defunct. Most of what we know as a “standardized” shotgun cartridge, was “fixed” around the time between the two World Wars. (More or less.)
The larger bores were in fact often used for “commercial” duck and goose hunting, and were not always shoulder-fired.
Long story short, with a few minor exceptions, anything but 10, 12, 16 and 20-guage, as well as .410, are considered antiques, curios, collector’s pieces, and so on. Few, if any, have been manufactured for some eighty years.
As for “kick”, that’s dependent on several factors:
Weight of the gun
Weight of the projectile(s)
Muzzle velocity and rate of accelleration.
Put it this way: if you fired a full-house 240-grain .44 Magnum from a compact, lightweight 2-1/2" barreled snubby revolver, it’s gonna knock ya down and stomp ya (as my pap used to say.
)
But if you fired it from a full-sized bolt-action type rifle, it almost feels like a squib load.
Same thing with the big-bore rifles: there’s a reason most of the .50 BMG rifles weigh upwards of 35 lb. 
Anthracite- Because the human holding the rifle and the rifle itself outweigh the projectile by a factor of two or three hundred.
Back to the topic:
Yes, current NFA rules prohibit anything over .500" bore diameter. Things like the .600 and .700 Nitro Express skim the rules by being a blackpowder/Pyrodex cartridge.
Shotguns have a larger bore but again pass since shotguns are considered their own category.
Badtz- I suggest some light reading on muzzle energy, velocity vs. recoil and projectile dynamics.
The infamous .577 Tyrannosaur- there’s a cool video out there showing a guy who can’t weigh 125 lbs shooting it (it gets the better of him)- has some 11,000 lbs of muzzle energy in a 13-lb rifle. The aforementioned videos show four different people shooting it, and not only surviving unbroken, but laughing about it afterwards.
Elephants exploding? Somebody’s been watching too much TV where gunfire from a handgun can throw a 200-lb man 20 feet backwards through a wall.
There have been numerous cases where an elephant has barely reacted to being shot with anything from a .338 to a .416 to a .585 Nayati. If you can’t afford an African hunting trip, watch the videos. Watch a Wildebeest take three shots from a .416 and only stop running because the third shot broke his shoulder.
As far as “Tremors” is concerned, I didn’t see the first one, but I did see the second. In that one, one of the good guys caps a monster-thing with a Grizzly bolt-action single shot in .50 BMG (Browning Machine Gun, basically a .30-'06 scaled up about 100%.)
The bullet 'splodes the beastie- of course- but then travels through a concrete wall, several drums, a shack and kills the truck they were trying to get to. 
The only problem is, the bullet would have only “exploded” the monster if it were an expanding bullet of some sort, which transfers far more of it’s energy to the target. More typically, a “ball” bullet, as in fully-jacketed and nonexpanding a’la the Geneva Convention, will zip in and zip back out the other side like a high-velocity icepick.
Yes, the target croaks but it doesn’t “explode”.
If the bullet does expand- and such an expanding bullet would indeed have popped the beastie like a ripe cantelope- it would NOT have then penetrated the wall, the drums and the truck.
Sorry about the novel, but too many people seem to take their firearms knowlege directly from the TV and “Mack Bolan” paperbacks. 