^the reason the commonapp is mentioned is that the colleges where it is a specific hook that can be as big as being a legacy are common app colleges; at these colleges, the definition used is “neither parent got a 4-year degree”.
The definition is wider at colleges where the large number of applicants don’t have parents with a 4-year degree. However there’s no question about being first gen - students must list their parents’ education and colleges can then decide what to do with the information.