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one difference would be that short forms are "shorter", while pet forms can be shorter, but can also be the same length or longer. And sometimes pet forms add diminutives at the end. And in some countries pet forms aren't used as real names, for example the common russian pet forms (like natasha), aren't really used as real names in Russia (afaik).

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I suppose sometimes it can be the same thing as well and both can be nicknames :)