I looked them up to see what they were and now I know why they're called pigs. There's a type of cheap clay used for small earthenware vessels in the way-back-when that used to be known as 'pyg' - pronounced 'pig'. It's the origin of the piggy bank because someone couldn't resist the pun, and now a vestigial lexical affect in the name of those salt pots.

::insert 'the more you know' gif::