Musing.io, busy.org, dlive etc. are Steem based applications and the interfaces of Steem blockchain. Everything you do on these applications are registered on Steem blockchain. But you need an account to be able to write anything on Steem blockchain through these applications.
Steemit.com was the first interface of this blockchain. It is used to open new accounts. With this account you can access the blockchain. Your Steemit account is the only account you need for this purpose. Musinig.io is not separate from the Steem blockchain. It runs on the same blockchain on which busy.org, steempeak.com, eSteem app etc. run. So, one common accounts is sufficient for accessing the Steem blockchain. That is why you cannot directly register on musing.io. You need a steemit account for that purpose.