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Could someone explain the nomenclature of the calibers used in these big naval guns, particularly the part about ".45 caliber", ".50 caliber", etc?

Caliber is defined as rifle length divided by bore diameter. In the case of the Iowas their rifles were 50x the diameter of their 16" bore, or just about 67 feet long.

The preceding Washington and South Dakota classes' guns were 45x their 16" bore, or 60 feet long. The extra 6' in length made a big difference in both distance and accuracy.

I've been aboard the Wisconsin (Iowa class) and the North Carolina (Washington Class) and my own Mk.I Eyeball observations are that the 6' difference is really noticeable - the North Carolina's guns look ... stubby ... compared to the Wisconsin's.

For naval rifles/guns, the inches is the inside diameter of the barrel. The caliber is the length of the barrel, so 50 caliber is 50 X the diameter. So, a US Navy 16”/50 gun means that the gun has a bore 16 inches in diameter, and a barrel length of 16 x 50 inches = 800 inches long.

This is different from the rifle you carry to hunt with, where a .30 caliber rifle means 3/10ths of an inch inside diameter, and a .50 caliber means a half inch inside diameter.