Banjoist: There was a very good article on the early Springfields in the "American Rifleman" (Monthly publication of the NRA with which you may well be familiar), particularly the experimental "ramrod bayonet" version. At first, this rifle was chambered for the ".30-'03" cartridge. Previously, in the era of black powder propellants, typical cartrige nomenclature consisted of the "caliber" or nominal bore diameter expressed in hundreths of an inch; ".45", ".32" etc., followed by the powder charge expressed in grains (1/7000 of an Ounce) of black powder. Thus ".45-70" implied a 45/100" diameter bullet over a charge of 70 grains of black powder. Sometimes the weight of the bullet was stuck after that, (.45-70/500) but you won't see that very often. The "Krag" took a ".30-40" cartridge, but that was the end of the reign of black powder in Military small-arms, and the cleaner-burning nitrocellulose "smokeless" propellants were not as consistant in weight/volume ratios as black, so the old system would no longer do.For the new high-power "Springfield", the cartridge (essentially a copy of the German 8 X 57 Millimeter - Europe was Metric and doing it's own thing with cartridge designations) was named aptly enough ".30 (3/10ths of an inch caliber)- '03" (abbreviation of the YEAR in which it was adopted for US Military Service. Now in 1906 they decided to change the bullet weight and shape a little, so the Army re-designated the round the ".30-'06"... and so it is to this day! So the expression "Ought-Six" referrs not so much to the rifle, as to the still popular and capable ammunition which it was designed to fire.
The "European" ammo designator referrs to the caliber in MM X the length of the brass casing (which is consistant; different bullet styles will effect overall length of the complete cartridge). Our "Modern" Military now uses the metric system, and so .30 cal. is now "7.62 MM" and .22 (M-16 etc.) "5.56 MM".
Shotgun "Guage" usually refers to how many lead spheres (balls) which will fit in the barrel it would take to make a pound. Thus, a "12-guage" is bigger than a "16-guage"... which is about .69" caliber, about the same as the bore on the Charleville muskets used in the Revolution, the round-ball lead projectiles of which weigh about an ounce. Go figure!