How does intelligence relate to being a genius?

Highest level. A person who is a genius has a level of intelligence in the very top range. The statistical normal curve goes from the bottom to the top range of intelligence. A person who is considered a genius will fall into the very top range of the normal curve.
Not always high IQ! The only real voyage of discovery consists not in seeking new landscapes but in having new eyes. -- Marcel Proust.
Formality. In a technical sense (as others have noted) genius refers to iq greater than 140, about 1 of 400 people. But practically genius is something else. After all, by technical criterion there are 750, 000 "geniuses" in the us! Rather, "genius is 1% inspiration and 99% perspiration. Accordingly, a 'genius' is often merely a talented person who has done all of his or her homework".