An on-chain transaction refers to a transaction that is recorded on the blockchain. This means that the transaction is publicly visible and permanently recorded on the distributed ledger, which is maintained by a network of nodes.

On the other hand, an off-chain transaction refers to a transaction that occurs outside of the blockchain network. This means that the transaction is not recorded on the blockchain, but rather, is settled privately between the parties involved. Off-chain transactions typically rely on other protocols or technologies to facilitate the transaction, such as payment channels or smart contracts.

One of the main differences between on-chain and off-chain transactions is the speed and cost of the transaction. On-chain transactions can be slow and expensive, especially during times of high network congestion, while off-chain transactions can be much faster and cheaper. Additionally, off-chain transactions can offer increased privacy and scalability, as they do not require every node on the network to validate and record the transaction on the blockchain.