Romance is the relationship between two lovers. Is there a romance blossoming between you and your lab partner, or is the assignment so hard you have to work together constantly?
Romance comes from Roman, and first meant a story translated into French from Latin (the common language of old Rome), usually about the amorous adventures of chivalrous knights, which is how romances came to be associated with love stories. Now it's used to mean a love relationship, in a story or not. The Romance languages are those derived from Latin. If you romance a tale, you exaggerate it, and if you romance a person, you're making advances.