Yes Short Pay and Short Sale are the same thing. Basically, the seller is asking their mortgage bank(s) to take less than they owe on the mortgage(s)-- so they will be paid short or the property will be sold short.
Yes, they are the same terms. Short sales or short pays can have promissory notes for deficiencies or other hooks past the close of escrow. A short sale/short pay is not a defined, established scenario. It is what the bank and home owner agree to while in compliance with governing laws.