Guarantor only guarantee the rent.
Co-signer is liable for rent, damages, fines etc.
Guarantor is liable for rent only after tenant won't pay. You might wait a few days or weeks, after exhausted all negotiation with tenant, before reaching out to guarantor.
Co-signer is liable for rent at the same time as tenant, the rent is due on the tenant AND the co-signer.
However, you can only sue anyone in their own state. So if co-signer or guarantor lives in another state, it's difficult to seek back rent. As long as the co-signer and guarantor live in the same state, don't need to be in the same county, you can sue them in local county court.