Fouling is the build up of firing residue.
Fowling is the hunting of birds for meat or feathers or other bird-parts.

Fouling won't be an issue for you if you are using smokeless powder in a cartridge gun.

If you are going to use (most) anything besides roundball, you will want rifling so that your projectile is stable and tracks relatively straight through the animal.

Smooth bore rifles do exist, although they do not seem to have been tremendously popular in the era of the metallic cartridge.