Okay got it.
So typically if you have multiple signatures (technically partial signatures not signatures but regardless) for a single wallet this will be a wallet that uses Multi-party Computation (MPC). There is no single key, but rather there are a number of key shards; of which a threshold number of shards have to be used to approve a transaction. The key shards are off-chain and the signing process is also off-chain taking placeat the cryptography layer.
Whereas, if you have multiple wallets controlling a single signature this will be a wallet that uses multisig.︀
MPC vs Multisig is a divisive topic, but for most use-cases I think MPC is︁ the better solution. A couple benefits you get with MPC that you don't get with︂ multi-sig:
- Blockchain agnostic; since MPC is off-chain, the same cryptography is used across all︃ protocols with the same signing scheme. This means that you have a narrower surface area︄ of attack than relying on the distinctive smart contract implementations of multisig on each chain︅ you want to hold assets on.
- native compatibility with all decentralized applications
- more︆ flexibility in terms of policy creation and access control
- lower transaction fees
- ability︇ to easily refresh keys...