Rule of law is the abstract idea, present in most Westernized liberal democracies, that all people, including the Sovereign (or the people running the Executive, Legislative and Judiciary branches of government) are equally subject to the law and have no further rights or duties than those set by the law.
Rule by law simply means that the country has some sort of legislative authority (whether it be the Sovereign or a specialized legislative branch), and said body's decisions constitute the highest level of hierarchy in a country's legal system except for its constitution.