How much of one thing per unit of another. A rate is only meaningful with both terms named.
Medieval Latin rata (a fixed portion), from Latin ratus (reckoned, fixed), past participle of reri (to reckon, to think); a rate is a reckoning fixed between two quantities, and it means nothing until both are named.
How much of one thing there is per unit of another. The root's reckoning needs two terms to mean anything at all, which is why a rate stated alone is really only half a sentence.