Listen at 2:07.
I mean, if we want to get technical, they're not exactly the same. They have identical melodic direction but, for the most part, they're separated by a 3rd. The Band Aid theme starts on Mi and the Independence Day theme starts on Do.
I brought this up to Colt the other day and said, "Don't you always think of Independence Day when you hear this song??" He said, "Not really." So, in order to prove to myself that I wasn't crazy, I wanted to post about it. Probably my most interesting post of all time actually.
Just know that for the rest of the Christmas season, every time I hear that star-filled group ask me if I know it's Christmas, I think of aliens coming to earth. And Jeff Goldblum saying, "Yes, yes, yes, without the oops."