It's shown they are distinct beings when Daimao implores his son to avenge his death and by numerous other pieces of dialogue that establish Daimao's evil was diluted by his "rebirth," and how Kami states Piccolo's father was the same being as him and not the son. I don't see how they necessarily have to be the same being when fat fuck guru gave birth to different types of Namekians as well while remaining a dragon clan member, and Daimao is simply Kami (a dragon clan member) split in two with an evil personality. He gave his reincarnation his memories, but they had different bodies and separate minds.
For instance, Super Boo has the same memories as Fat Boo and speaks as if he committed all of fatty's actions himself, but his body changed to become more battle-oriented. Similar concept here.