On-chain transactions take place in the blockchain. By its nature, it’s irreversible, near-instant, and can be executed at any time, to anyone. There is no need for authorization or intermediaries. Once validated and entered into the ledger, on-chain transactions are pretty much irrevocable and can’t be “lost” or removed. On-chain transactions on Public Mint have transparent, low fees.
Off-chain transactions happen through traditional banking settlement layers. Funds are transferred across banks and may take days or in some cases even weeks to clear. Such transfers can usually be arbitrarily declined or even reversed with no clear reason, and funds in transit can be misplaced or even lost. On top of that, fees charged are usually unpredictable and can be quite steep.