Is the student with the highest grades the most intelligent?

Sometimes, yes, but by no means all the time. Often, the most intelligent person in the class gets the highest grades. But fairly commonly, the most intelligent person doesn't get the highest grades, or any more than average grades. And occasionally, the most intelligent person in the class gets the lowest grades, for their own reasons. Now, consider the hardest working person in the class. Sometimes, they'll have the highest grades, sometimes they won't. But they will never have the lowest grades.

Quantifying intelligence is nearly impossible. That's what grades are for. While good grades is a fair indicator of intelligence they also require hard work which is another admirable character trait. There are plenty of lazy intelligent people and plenty of middle of the road PhD's. You can look at intelligence as a muscle. If used and exercised it is fully functioning but if unused or let to atrophy it becomes flabby and out of shape. So, the reason for grades is not necessarily a measure of intelligence as much as a measure of work ethic.