Do you actually sign into Outlook.com with your gmail account, or are you just reusing credentials to sign into a separate account on Outlook.com? I'm not sure that the two systems federate, but I've got an Outlook.com account that uses my gmail email address as the username, but the account is completely separate.
That's using your Google account, with Google's OAuth, to get into an Outlook account — which is still weird and confusing, and IMO something Microsoft shouldn't have done because it'll confuse people, but hey.
I was thinking whether I should add a remark that you can add your Gmail account to outlook.com as well, but I didn't want to over-complicate it. In the end, both Outlook (the program) and outlook.com are mail clients of a sort, the latter being a webmail client.