Respectfully, they are quite different. A co-signer is generally used only if the first party can't pay rent. A guarantor is used regardless of ability to pay and is explicitly designed to make sure that only people with appropriate social status are allowed to live in the building.

Not sure what a guarantor fee

If you're unable to come up with a Japanese company to guarantee you because of social ties, you can pay a company to do so. (This is, ahem, often necessary but insufficient to pass the must-be-at-least-this-social-status-to-rent bar.)

It's basically a surety bond: they promise my landlord one month's rent if I skip out. This bond costs me precisely one month's rent and is nonrefundable, much like an insurance premium. (Warren Buffet just said "Eff me that's the most profitable insurance policy in history.")