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Jel posted about a difference of 7.5", but you also have to remember the the bases are positioned with a corner pointing to the pitcher, where the plate has a flat edge toward the pitcher, so the distance could deviate depending on the angle.
From what I have read, the first baseball games were played with the three square bases centered on three of the corners of the square, and with a round plate centered on the fourth point. The article I read speculated that to aid in determining whether a ball was fair or foul, first and third were moved solely into fair territory. Eventually the foul part of the plate was done away with, and it was squared off. Second base was left were it was, centered on the right angle of the square.
Then after many years of everyone being satisfied with the layout, someone decided that they again wanted to put part of the bag in foul territory. They decided it would work beautifully if they only painted it orange, said they were doing it for safety and told everyone that it disappears after it gets used.
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