There are thousands of quite unrelated families called Smith. The reason for this is that in the Middle Ages, which is when English-speaking people adopted surnames, every village needed a smith, but usually just one. The smith had a very important function in the community, so when you needed to distinguish him from all the other men with the same given name in the village, it came naturally to everyone call him Thomas Smith (rather than something like Thomas Johnson after his father, or Thomas Long for his height, or Thomas Hill for where he lived) and call his family the Smith family.
The same thing happened in many other parts of Europe: there are thousands of Germans called Schmidt, Spaniards called Herrero, Hungarians called Kovacs, et cetera: all these surnames mean 'smith'. And no, they are not all related to each other, either.