Anyone who has had a quicky had a non-romantic sexual relationship.

Going the other way, romance is much richer than just sex. If a man and a woman go out to dinner, talk late, enjoy each other's company, hold hands and are otherwise intimate, I'd call that a romantic relationship. If there was no kissing, fondling, sex etc, then I wouldn't call it a sexual relationship. Openminded adults usually progress from one to the other, but not always. For one thing the romance could break off before it naturally progressed. Or one or both parties has strong convictions about sex outside of marriage.

Cheers,
Ben