Essentially, a guarantee assures a customer that a purchased product or service will meet certain requirements for a set period of time. For example, a flooring company might guarantee their craftsmanship for a year after installation.
Warranties are also part of the sale of goods and services. Warranties come in a variety of different forms, but at their heart they are a statement about goods, services, or the conditions of a product made by one party that can be accepted as truth by the other party.
Written warranties also usually cover a good no matter what happens to it, while guarantees generally provide out-clauses if damage is caused outside of normal conditions. For example, in the case of the flooring company mentioned above, a company might guarantee their flooring for up to two years.