A Madeira account is an Office 365 account, also known as an “work or school account”.
If you are using your Microsoft Account to sign up for Madeira, you are actually adding a “new” Microsoft Account to your email. So the next time you log in with that account, you might be see this:
The top one, is the new “Office 365” account, and the bottom one is your old Microsoft Account. Confusing 🙂
So, if you have an Office 365 subscription, use that account for Madeira, that will give you the option of trying out the Outlook integration pieces and avoid creating another account.