No, .24 caliber certainly does not equal .50 caliber.
.25 is 1/4 of an inch, so .24 is slightly less than that. If I recall correctly, number 4 buckshot is .24" in diameter.
.50 caliber is 1/2 inch.
If a bare .490 ball rolls easily down the bore, but a .530 ball stops just an inch down from that belled muzzle, then I would guess that you have a .50 caliber blunderbuss.
The gun looks shootable in the picture, but check it out first. Run that ramrod down the bore to be sure it hits the breech plug and you know the gun is unloaded. Then see if you can run a patched .490 ball down the bore. It should be tight, but go down easily. Don't use too much force. You can then use a ball puller to get the ball out.
If that works out okay, then I would first snap a cap or two to make sure the passage is clear. Next load a small powder charge of only 20 or 30 grains, and a patched ball. Set the gun in some makeshift cradle on the ground and pointing into a good, solid backstop, put a sandbag or something similar over the gun to hold it down, tie a cord to the trigger and step back 15 or 20 yards. Then pull the cord to set the gun off.
If all goes well, you can then try the same method, but with a heavier powder charge. But, I don't think that I, personally, would want to go over 60 or 70 grains in that gun.