Rules are instructions for a place or situation, such as school, home or sports teams. They can be made by people who have authority, such as teachers, parents and coaches. Sometimes they are made with the input of the whole group.
Rules are not legally binding and only apply to people who are part of that group with the rules.
Both refer to a set of principles designed to govern something.
Laws are binding rules. They are put in place by the Parliament and carry with them the power to enforce penalties for refusal to obey them.