Indemnity and Guarantee are both widely used in commercial transactions all over the world. The term Indemnity is defined in the Section 124 of the Indian Contract Act 1872 while Guarantee is in Section 126 of the same act. 

Both the terms by definition seem synonymous but they are not. 

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Guarantee

Guarantee is the promise of person to fulfil a particular obligation of a certain party in event such party is fails too. Here, the contract entered in to are three. One between the principal debtor and creditor (regarding the existing liability), Creditor and the Surety (laying down the obligation of the surety) and lastly, between the principal debtor and the surety (signifying that the latter shall act as the surety).  Guarantee may be given in written or oral. 

Here, liability already exists and the contract involving surety shall come into operation only when the debtor fails to met his obligation. It is to be noted that the obligation is certain and the surety usually knows what he is getting into and what exactly is the obligation he is to fulfil in the event the debtor fails. 

A simple example to understand this is, A takes a loan from B wherein C is thee surety. Here, A, of course, is liable to pay the amount to B. And only if he fails, C becomes liable and that too only for the amount owed by B in respect of loan and not any ancillary costs like legal expenses unless the same is agreed to while entering into contract.

Indemnity

Indemnity is again a contingent contract which comes into operation when event of loss occurs. In indemnity one party agrees to indemnify (make good/compensate) another party in event of any loss in relation to the contract. A single agreement exists between he indemnifier and the indemnified. The most common phenomenon wherein indemnity is prevalent is insurance. When a person takes a medical insurance for an amount of premium, the insurer shall indemnify i.e., compensate the insured as against all the expenses incurred in the medical case. The contract be written or oral. 

Liability of the indemnifying party arises only when the event triggering the loss occurs. Further, the amount of liability is not very certain and the indemnifier agrees, for consideration (premium in case of insurance) to compensate irrespective of the amount of loss. 

Key differences

1. The purpose of guarantee is to secure the interest of the creditor, i.e., to ensure that the contract is fulfilled. On the other hand, the contract of indemnity is entered into so as to protect the promisee against some likely loss.
2. Guarantor guarantees only completion of the contract on behalf of the debtor while the indemnifier promises to compensate for all losses suffered due to the act of any third party.
3. In guarantee, liability exists right from the beginning. That is, the creditor is entitled to receive money right when the contract is entered. But in case of indemnity, there is a contingency as to whether liability shall arise. The liability arises only when loss is suffered by the indemnified party. 
4. The number of contracts entered into for guarantee are three, while for indemnity it a single contract.
5. The liability of guarantor is secondary, ie primary liability is of the debtor himself and only if he fails, the guarantor steps in. But in case of indemnity, the indemnifier is liable primarily. 
6. Guarantee is defined in section 126 of the Indian Contract Act, 1872 while Indemnity is defined in Section 124. 
7. The guarantor on completing the contract due to failure on the part of debtor can later on seek compensation from the debtor. But indemnifier holds the final burden in case of indemnity.

Thus, though both the terms may seem similar but they bring about a marked change in the liability of the parties to contract.