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Black
The usual way of shortening "Blacksmith" was to "Smith." However, in a city that might have goldsmiths and silversmiths, "Blacksmith" could be shortened to "Black" to avoid confusion. Our one family split into these two names sometime in the Middle Ages.
Smythe
When the name "Smith" was first written down, it would have been written by Norman-French clerks. They would have written it as "Smythe", although still pronouncing it "Smith." The great majority of our family would have to wait for centuries before they could read and write, and they then spelled their name as "Smith" in normal modern English. However, the more well-to-do of our family would have been writing their name "Smythe" in the Middle Ages, although pronouncing it "Smith." They kept the spelling, and as the English language grew more modern, they started to change the pronunciation of their name to suit the spelling, so that it rhymed with "hive." This explains why the Smythes have traditionally considered themselves to be a better class of Smith!