No difference. Gays are not looking for anything extra. Just the same as everyone else. The right to work without discrimination. The right to marry the person we love. The right to show appropriate affection in public. Et cetera.
Human rights are directed at all people. Whether black or white, muslim, or Jewish. Where as gay rights are directed mainly at transgenders, gays, lesbians and so on.
Denying basic civil rights to gay people does not add anything to the public good. However, extending equal civil rights to everyone improves the quality of life for all.
The difference is that most of the opposition to gay rights believes being gay is a choice (and a bad one at that). No one in the racial civil rights era believed being Black was a choice.
There is a difference
none
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there both gay there is no difference at all
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The difference between straight and gay partners is their gender attraction. Straight people are attracted the opposite gender for their partners, whereas gay people are attracted to their own gender.