On-chain governance means proposals and votes are executed directly by smart contracts — if a vote passes, the code changes automatically. This is fully transparent and trustless, but it is slow, expensive to participate in, and vulnerable to low-turnout attacks where a small number of large holders can push through proposals.
Off-chain governance uses platforms like Snapshot for gasless voting, with the results executed by a multisig or core team. This is cheaper and more accessible, but it introduces a trust assumption: someone has to implement the result of the vote, and they could choose not to. Most projects use a hybrid — off-chain signaling for non-critical decisions, on-chain execution for treasury disbursements and protocol parameter changes. The right mix depends on your protocol's maturity and your community's engagement level.