A price refers to a fixed amount of money.
A rate refers to a set amount of money which is charged according to some period of time or some number of items.
He is charging $50 - I pay him 50 dollars.
His rates are $50 per hour. - The amount that I pay will depend on how long he works. If he works for 2 hours, I pay him 2 X $50 = $100
The rate might also be per some item.
If a customer contracts for wheat at a rate of $10 a bushel, the final amount will depend on how many bushels of wheat I can deliver.