Off-chain transactions: These are the transactions dealing with the values outside the blockchain and can be carried out using different number of methods. First of all, two parties can have a transfer agreement. Second, a third party might exist who guarantees that the transaction is complete and correct. The third party is some sort of a guarantor in the transaction. Today, payments processors such as PayPal work along these lines.
Off-chain transactions are executed instantly as compared to the on-chain transactions that can lag for a long time depending on the number of transactions waiting to happen on the same network as well as the network load and the transactions on the queue not yet confirmed.