A guaranty is an undertaking to meet a payment or other obligation on behalf of another. It's usually made in writing. More than one are known as guaranties and they're made by a guarantor.
A guaranty can also be something used as security for a guaranty. So a guaranty should, in theory, guarantee that the guaranty is met.
Confused yet? If so, don't worry about it and stick with guarantee. That can be used instead of guaranty as well as meaning a formal promise or assurance.