They are both verbs and nouns and are used in various commercial contexts in different ways. The general idea of both is to pay for borrowing something. Leasing generally implies a longer period than renting. For example: a) You "rent" a flat for 6 months b) You "rent" a car on holiday for 2 weeks. c) A car company "leases" your business a car for your professional use. d) You buy a "long lease" of a flat (apartment) in a block of flats for 99 years. The usages may be a little different in N America and elsewhere (I am from England).

Lease is a contract that allows you to use a building, land etc. for a period of time, for which you pay a rent. Rent is the amount of money you regularly pay in order to use a house etc., as determined in the lease agreement.