Anniversary of your birth! Technically, if you say "Happy Birthday" then you are saying Happy day of your birth meaning your congratulating someone on just being born that day in that year that you say "Happy Birthday." It wouldn't make sense to say "Happy Early Birthday" unless you're saying it to an unborn baby but it would make sense to say "Happy Late Birthday" to anyone though!
Saying Happy Anniversary of your Birth is congratulating a person on being alive for __ years and how many years it was from their birth date.
Idk guys, my teacher said it to the class in 5th grade and it stuck with me ever since even though I still say "Happy Birthday" because that's what people understand. Just like weighing yourself and you get your "weight" it's not actually your weight, it's your mass which is two different things. People don't usually say "what is your mass", others might get confused by that. 
