Of course it is a competition, otherwise you could just sign up for classes. The issue is who is the competition, just others from your high school, town, or state, or the entire world? I don’t think it is head to head for every spot, but there are general pools and the competitive schools are not going to take the entire pool from your high school or the entire pool from your town.
Columbia tells the NYC students from the test in high schools that they aren’t all going to get accepted even though many of the will have close to perfect scores and gpa’s. Yes, they are competing against each other.