This is actually a good question because there are probably overlaps between the two. But norms are usually unspoken agreements about behavior that all the people in a particular group or setting adhere to. Rules are usually explicit, most likely written down, and not always immediately obvious ways to do things. For example, one NORM when entering an elevator is to turn around and face the front. Nobody tells you to do this, but it's an elevator behavioral norm. But a company may have a RULE that only certain people can use certain elevators, such as in a hospital where there are elevators for medical staff, and those for visitors.
Another example for a norm is that employees in a business tend to avoid the boss, while a rule in this business might be that employees are required to meet with their direct supervisors once a week.
Another example for a norm is that employees in a business tend to avoid the boss, while a rule in this business might be that employees are required to meet with their direct supervisors once a week.