I am using desktop notebook with windows 8.
I use Outlook 2010 as my mail, calendar and contacts. I then purchased a windows phone and synched my contacts and calendar using Hotmail address/live account and Hotmail connector.
Since then I upgraded Hotmail acct to outlook.com (didn't change my address) and sometimes send mail through my phone and notebook using my Hotmail address.
If I am in my windows 8 screen (not desktop) and I select my Mail app I get a screen that shows my inbox,
on the top left hand side of the screen it shows as HOTMAIL with three option on right hand side New ,respond, Bin. 13 messages including Hotmail address mail and calendar show with no second page available. I have since worked out how to change the number of days I get mail so number of mails is not an issue.
If I log in to Hotmail or live acct via IE I go to a screen that says OUTLOOK on the top LHS of screen with further options under the email file folders with more option on right of screen
To me appears as if I am directed to a Hotmail account from the Mail tile on my screen and not to my Outlook.com account.