When you want to send funds from your wallet, you create and sign a transaction, effectively stating that you are the owner of this wallet. Single signature cryptocurrency wallets need one signature to sign a transaction.
A multi-sig wallet requires one or more signatures to sign a transaction.
A multi-sig wallet set up such that it only requires a single signature is just a special case of the multi-sig and the owner will most likely configure it to support multiple copayers.
A multi-sig wallet is a wallet shared by two or more users called copayers. Depending on the kind of wallet, the number of signatures required to sign a transaction will be lower or equal to the number of copayers of the wallet. Multisig wallets are often designated as m of n, where m <= n and it means that n copayers are set up for that wallet and m distinct signatures are required from the list of copayers.
For example, a 3-3 wallet is a multi-sig wallet that is shared by three people and requires three signatures to sign a transaction.
A 2-3 wallet is a multi-sig wallet that is shared by three people and requires two signatures to sign a transaction.