Please consider this scenario. I agree with other party that we will create 2/2 multisig wallet, so we can only spend funds from that wallet together. The other party will create its wallet, generates first key as her/his own (public+private) and then imports my public key as second key. That is correct 2/2 multisig wallet.
But I will create 2/3 wallet on my side. I will generate two own keys and as third key I will import public key of other party. That means I can use only my own keys to fully sign the wallet.
Will both wallets see funds when one of us will deposit? In theory I could then withdraw funds only myself, because I have necessary two keys of three, while other party things the wallet is 2/2. Or will these be two different wallets?