Not all states have a "long form" and a "short form." Where they do, as in the case of Hawaii, the short form is based solely on information from the long form, so there is no contradiction between...
You can get a certified copy of your birth certificate from the county where you were born. Most counties have it available to order on line now. Try searching for county, state on yahoo or google or...
Not all states have long/short forms, but you do need a passport and to get that you have to have a birth certificate. As long as it is from the state where you were born it doesn't matter the length...