Is there a difference between a corn and a callus?

Not much. The terms "corn" and "callus" can be used interchangeably, but podiatrists use "callus" to describe a buildup of skin on the bottom of the foot or heel, and "corn" to describe a callus that forms on a toe.
Yes there can be. Corn is a hard localized and more defined skin lesion, callus is more diffuse under a bony prominence.