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1.
One's natural preference in romantic partners, not to be confused with sexual orientation, which is one's natural preference in sexual partners.
Joe: I hate girls so much. They disgust me!

Jim: Really! I always thought you were straight! We should go out someday. We could hook up!

Joe: No. I'm not attracted to men. My sexual orientation is straight, but my romantic orientation is neither. I want to fuck girls, not have a relationship with them.
by rogerthewale January 18, 2013
 
2.
Just like your sexual orientation describes who you can be sexually attracted to, your romantic orientation describes who you can be romantically attracted to.

A lot of people are pariorientated, meaning there sexual and romantic orientations match. (For example a heterosexual heteromantic) But sometimes people are variorientated, meaning they have differing sexual and romantic orientations. (Such as an asexual heteromantic)

Although people often talk about sexual orientation more than romantic orientation, the truth is romantic attraction is usually more important than sexual attraction, as it has a stronger influence on who you will form relationships with and marry.
Friend 1: "I've always wondered, what is your sexuality?"
Friend 2: "Why do you wonder that, doesn't my romantic orientation matter more? I'm not going to marry someone just because they're sexy."

"I don't care who anyone is sexually attracted to, I'd rather know what your romantic orientation is if you're willing to tell me."

"I'm asexual but I do experience romantic attraction."
by N9GB June 11, 2014