There is no difference. None whatsoever. Zilch. Nada. From the point of view of a just government - there is absolutely no possible difference. 
Opposing one is just as evil as opposing the other - and you have every right to oppose both or neither - but when somebody tries to use the law to force others not to engage in a variation they oppose, that's where the line is crossed from just being an objectionable asshole who deserves to be mocked, scorned and cast out of society - to becoming an authoritarian evil who must be fought, violently  if need be, for the preservation of liberty and equality before the law.

This is the sort of thing revolutions are justly fought over.