This is an interesting question. Bear in mind, this is strictly a muzzleloading forum, and topics pertaining strictly to breechloaders are not discussed here. However, the topic of caliber has some overlap between breechloaders and muzzleloaders, so here goes....
Bore size for muzzleloaders is generally accepted as land-to-land diameter. Cartridge shooters consider bore size to be bottom of groove to the bottom of an opposite groove. This explains why a .44 caliber cap and ball revolver can be converted to shoot .45 Colt or Schofield cartridges simply by swapping cylinders. The Dixie Gun Works catalog tells us that the Uberti Walker and Dragoon revolvers have a land-to-land bore diameter of .440", making them .44 caliber blackpowder revolvers. The grooves are .008" deep, so the bore diameter of the same revolvers, measured from the bottom of one groove to the bottom of an opposite groove, is .456", which would be .45 caliber to a cartridge shooter. Most of the Italian .44 caliber cap and ball revolvers have a land-to-land diameter of .440", but groove depth varies. This can affect your choice of ball size for these firearms, as well as compatibility with cartridge conversion cylinders.
It gets complicated. I think the modern metric calibers are measured from land to land, like muzzleloaders. For example, 7.62mm calculates to .300", or .30 caliber, which is why the 7.62x51NATO round will interchange with a .308 Winchester. To complicate matters further, the nominal caliber of a cartridge gun is not necessarily the same as its bore size by actual measurement. A modern .44 Special, for example, typically has a bore size (bottom of groove to bottom of groove) of .429". But that's all we are going to say about that.
Muzzleloading barrel and rifle makers do appear to have standardized some bore sizes these days, e.g. .40, .45, .50, .54, .58, and .62. Old-time rifle makers were not necessarily bound to these standards, which is why you see older muzzleloaders in calibers like .41, .47, or .52. Back in the day, it was also common, if not typical, to refer to "balls to the pound" ("gauge") as a measure of caliber, although it is not always clear whether the writer was referring to the actual bore size or the ball size. The difference between ball size and bore size is called "windage". A round ball that is meant to be shot with a patch, frequently abbreviated as PRB (for "patched round ball") on this forum, is of a diameter somewhat under the land-to-land bore diameter of the rifle. Windage may be as much as .020" or as little as .001", or even 0.00" (bore size), depending mainly on shooter preference, and patch thickness varies accordingly. In tenngun's post (above), he reports using a round ball of bore size for best accuracy, but it was understandably hard to load, so he selected a slightly smaller ball .005" under bore size as a compromise. A smaller ball will need a thicker patch to effect a gas seal. Please refer to plmeek's excellent summary of ball size and gauge in the "Rocky Mountain Fur Trade" section of this board for further discussion of ball size and gauge.
Thanks for introducing this interesting question.
Notchy Bob