come on, someone has to know!
Are you talking about something like cash and carry arb? I suppose you could say the return rate in the long leg is the cash rate and the rate implied in the short leg is the carry rate. Thus the carry rate is the rate that it costs you to finance and store something (gold is always a fine example) and cash rate is the rate you earn by buying a futures contract (or similar). If the market is arbitrage-free (and complete or tradable) these should be the same.