The Money Trough is not a pet and cannot be placed into the pet equipment slot.
It can be used to store situational, less-used items, e.g. hammers, potions, fishing equipment, or alternate armor or weapons, which would otherwise clog up inventory space.
The Flying Piggy Bank is an allusion to the phrase when pigs fly, a figure of speech used to humorously describe something that is thought to be impossible or will never happen.
Desktop 1.4.0.1: Can now be dropped by Wandering Eye Fish and Zombie Mermen.