Utility token: these are used much like traditional FIAT money - tokens that are used to purchase a service, units or services. You can compare them to having the key to accessing the service.
Security token: these tokens are usually compared to owning shares in a company but it is not really the same as no one legally owns the company. They are used for voting on decisions or paying our dividends to token holders. Normally refered to as a decentralized autonous organisation: a DAO.