in bitcoin there is no "addresses" to be single sig or muti sig or be tied to something! an address is just an abstraction to make things easier for the end user to work with also they are human readable.
in bitcoin we only have transactions and a transaction has a part in it (the tx_out) which is creating a locking mechanism that can only be unlocked with a certain cryptographic method.
for example what you see as "normal" addresses that start with one are actually a mechanism called Pay to Pubkey Hash outputs. and to spend these transactions you have to "unlock" them you have to provide a digital signature that matches that mechanism. if you look under the hood the mechanism is this:
(signature)(public key)(duplicate public key then hash)(compare with hash that we have from previous tx)(if ok then check the signature)
the mechanism for multi signatures are the same but has additional steps
(multiple signatures)(a script which is created with multiple public keys)(duplicate previous item and hash it)(compare with hash that we have from previous tx)(if ok then check signatures)
now you can change that "script" (the second item) to anything you want. think of this whole thing as running a programming function that you are writing. when you change that script you are changing the unlocking mechanism. it can be a mechanism that requires 5 signatures from 15 keys, it can be 1 signature from 1 key, it can be a condition like a hash function that doesn't even need signatures (although this will be non-standard).
for example you can create a transaction like this:
(some arbitrary data)(duplicate the previous item and hash it with SHA1)(compare the result with the hash that we have from previous tx)(if ok then spend the funds)
[OP_DUP][OP_SHA1][OP_EQUALVERIFY]
What is the difference with this and a regular wallet?
it makes perfect sense! haven't you seen the workaroud for SegWit aka P2SWH?
what you are calling 1 of x is jut another script that instead of multiple public keys, has only one