ClaireBear is correct. From the Oxford English Dictionary- Cater means to go diagonally, and has been used in English since the 16th century at least. From the French quatre.
Caterways, catercorner, etc. seem to be 19th century in print but could be much earlier. Caterwise is known from Sussex.

The OED also says now chiefly U. S., although the words originated in the British Isles.