Answer
A guarantor binds himself to pay the creditor only if the principal debtor fails to do so and cannot pay; his liability is subsidiary and secondary, and he is entitled to have the debtor's property exhausted first (the benefit of excussion, Civil Code Article 2058). A surety, by contrast, binds himself solidarily with the principal debtor: his liability is direct, primary, and immediate, and he is not entitled to the benefit of excussion.
What controls is the substance of the undertaking, not its name. A contract denominated a guaranty but in which the party binds himself solidarily with the debtor is legally a suretyship. It is often said that a surety insures the debt itself, while a guarantor insures only the solvency of the debtor.