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As well as a name, it's a dictionary word, meaning a fox, so it came to be used as a surname in the same way that Fox did. Then like some surnames it came into use as a given name.

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There is what looks like a longer version of the surname: Todhunter. But it just means what it says - someone who hunted foxes. The Tod- component came first, in other words.

Usually Todd and Tod are transfers from the surname Todd (meaning "fox", as Anneza said) and are not short forms of a longer name.

Well, perhaps in some instances it could also be a variant form of Tad (short form of Thaddeus) or Ted (short form of Theodore). :) Especially since the pronunciation of Tod(d) and Tad can be very close in some areas.