@Stanccepted, you’re right that different schools have different rules on EA so it can be a bit confusing. The posters above have noted how it works at Stanford and it’s similar with the EA programs at HYP.
There are also schools with open EA, such as Chicago and MIT, as well as ED schools (such as Dartmouth) that allow applicants to apply EA elsewhere, but they must attend the ED school if accepted there. There are also schools with multiple rounds of EA or ED.