What is the difference between haemorrhoid and rectal prolapse?

Two completely different things. Hemorrhoids are places at or in the rectum or anus where veins have become swollen into lumps. They may be benign or cause pain or itching. They may be internal or external.

A rectal prolapse is where the rectum itself (not just veins) has partially exited the anus and hangs down. In such a case, a doctor should be consulted immediately.