Man Vs Man: conflict between Tybalt and Romeo. Romeo gate-crashed the Capulet party. Tybalt Capulet considered that action as a great dishonor to his family. He decided that Romeo had to pay. He commanded Romeo to 'turn and draw', taking part in a duel.
Man Vs Society: conflict between Romeo and the Montagues, his family. Romeo knew his family was at war with the Capulets. He should hate all memebers of the Capulets. Instead he fell in love with Juliet. His actions went against his family's wishes.