On-chain transactions refer to cryptocurrency transactions which take place on the blockchain.
An on-chain transaction occurs when the blockchain is modified to reflect the transaction on the public ledger.
It involves the transaction being validated and authenticated by a suitable number of trusted nodes, recording of the details of the transaction on the suitable block, and broadcasting of the necessary information to the whole blockchain network, which makes it irreversible.
Off-chain transactions refer to transactions on a cryptocurrency network which moves the value outside of the blockchain.
On-chain transactions where the validity is authenticated via a suitable number of participants (through recording of the details).
In comparison, off-chain transactions take the value outside of the blockchain and can be executed using multiple methods. In most cases, off-chain transactions utilise a third-party guarantor who guarantees to honour the transactions, for example, services such as PayPal.