There is a huge difference between these two things.

One involves an actual belief system involving and a whole host of doctrine, dogma, and adherence to the words of a book written thousands of years ago proclaiming to be the word of a (possibly fictitious) supernatural being that is claimed to have the ability to punish people with eternal damnation if they don't follow his rules. Such belief systems frequently require the believer to be bigoted towards certain groups, to demand that society as a whole conform to their religious law, and to reject certain aspects of science that conflict with their beliefs.

The other is basically saying, "Hey, these are real people that deserve to be treated with dignity and respect as well as deserving of equality under the law, and NOT treated like second-class citizens or worse simply because they're different."

Why do sexual orientations even need flags? What's the purpose?