What's the difference?

Compare 'long-form' Hawaiian birth certificate with Obama's

Here is an actual Hawaiian birth certificate from 1963 (the same era as Obama's birth), which while redacted includes detailed information documenting a birth, including the name of the birth hospital and the attending physician. Beneath it is the short-form "Certification of Live Birth" offered by President Obama as proof of his Hawaiian birth. It is possible to have been born outside of Hawaii and still obtain the latter form, but not the former:

Here is the "Certification of Live Birth" presented by Obama