As you know by now, the ancient Romans adopted nearly all of the ancient Greek gods. They gave them Roman names and Roman personalities. For some reason, the ancient Romans never change Apollo's name. So, the god is Apollo in both Greek and Roman mythology.
Apollo had lots of jobs. He brought up the sun. He watched over music and musicians. He put up with his little brother, Mercury (Hermes to the Greeks - same god, different name.) He loved his mother. He even got along with his twin sister, Diana, the cold goddess of the hunt. He had a mortal mother, but his father was the mighty Jupiter (Zeus in Greek) - king of all the gods.
Apollo was a gentle god. But he could lose his temper if provoked enough. When he did, Apollo always got even in clever ways.