rent = occupy or use something (land, building, car, etc.) for rent (payment)

• We don’t own our house, we rent it from Mr. Jorty
• On vacation to Bangalore, we rented a car to get about
• There are villas for rent in the city

rent out = allow someone to use something in return for payment

• My brother has a villa that he rents out to tourists
• The company rents out office space to business
• She rents out one of her rooms to students
• If you don’t want to sell it, why don’t you rent it out?