Local key types are Secret Network keys owned by a secretcli user (i.e controls the private keys). Local accounts are made using the secretcli keys add <alias> command.
Multi key types, are Secret Network keys representing multi-signature wallet addresses. They are generated using the secretcli keys add --multisig=name1,name2,name3[...] --multisig-threshold=K command.
Offline key types are Secret Network keys that are imported into a secretcli users keyring, but NOT owned by the user. They are generated using the secretcli keys add <alias> --pubkey=<public_address_key> command.