Have Sex is a phrase that describes physical connection that leads to sexual pleasure, release and gratification. Making Love is all of this, but also emphasizes the deep emotional connection, affection and shared bond that develops between caring lovers. While making love is also to do with the state of mind, having sex is more about the physical relation.
Having sex is general sexual intercourse between a couple. This is irrespective of the fact that they share love or any bond between them. While making love reflects a feeling of affection associated with sexual intercourse. Making love also implies being intimate with your partner, not only physically but also mentally while having sex is just an urge for intercourse.
One may have sex with any person, needn't be their partner, spouse, beloved etc. It can also mean casual sex with anyone. While making love is generally referred to intercourse with a partner, spouse or beloved. In simple words, with one you care for or are emotionally attached to.
Having sex doesn't extend beyond sexual intercourse and more often than not, there isn't any emotion between the couple. On the hand, emotional attachment, including infatuation in the beginning of a relationship, is there when making love. It is sharing over all intimacy. Some people also suggest that making love is an expression of love though having sex isn't because love might not be involved.
Having sex may just satisfy one's sexual urge while making love may please a person's physical, emotional, sexual and mental urges. It can be said that having sex is merely restricted to a physical act while making love goes to include other urges also.
A few people also might believe that having sex is when sexual intercourse is fast and quick while making love is when they're having slow and tender sexual intercourse.