Emails to my @outlook.com do not arrive at my @hotmail.com. Even though it’s the same user name.

When I check my inbox @outlook .com all my @hotmail arrives there (or my junkbox), but when I send to the same using @outlook, it doesn't get there . I gave the Bank my @outlook and I'm worried their statements won't arrive. I cannot independently go to my @outlook account without going to my @hotmail,. That's fine, because I always thought they were one and the same, but now I'm confused. It's the same xxx@outlook user-name. I have no other aliases.