The difference is that there is at least a reasonably well-established precedent for Presidential candidates to release tax returns stretching back to the 1970s. Ironically, Mitt's father was the first to do so and establish the precedent, if my memory is correct.
Also, Presidents listen to and act on behalf of a variety of special interests. It is of some interest at least to see which of these special interests he benefits from in terms of his own personal income. It is also useful to know whether President's are vulnerable to financial or tax scandals. It is a legitimate part of a thorough vetting process that has bi-partisan support among wide swatches of the American public.
In contrast, there is no precedent to releasing birth certificates and no bi-partisan demand to do so, or demand among reasonably rational people.
So the one is an established practice deemed useful by members of both political parties as part of the thorough vetting process of presidential candidates. The other was a witch hunt by a bunch of paranoid, irrational looney toons.
I believe that equating the two is making a false equivalence.
Hillary Clinton would have been president if these standards were applied in 2008 (democrat would have won regardless being assumed).