The words "price" and "cost" are very close in meaning, but there are slight differences. "Price" emphasizes how much the seller has decided to charge for something:
I don't usually shop there. Their prices are high.
"Cost", on the other hand, emphasizes how much you pay for something:
It's a fun city, but the cost of living there is so high!
So you can use both words in the same sentence to compare the "price" of something with its "cost":
The original price was $120, but it only cost me $90 because I had an employee discount.