Both versions are "real". What you posted is the form filled out in 1963. But if you were born in Hawaii and you submit a request for your birth certificate, the one like Obama posted is what they send. The data on it comes from the original. It is just as "real". It is an official certified birth certificate that can be used for any purpose requiring a birth certificate.
Just last month I had to request my own birth certificate from California and they automatically sent me the long form version. With attending physician's signature. It is a copy of the original from microfiche that is printed on modern paper, with a raised seal and sig of county recorder.
That piece of worthless paper Obama posted to his website wouldn't even let him back in the country if he wasn't "The One."
Actually, the state department requires a long form BC to get a passport. It’s on the web site.