Rule of Law" [1] [2] is very different from "rule by laws".
Likewise, "government under law" differs from "government by laws".
The Russian pravovoe gosudarstvo is often translated as "government under law" but is usually interpreted to mean, essentially, "government by laws" — which, of course, is a great improvement over a system in which officials act without reference to laws.
Although an improvement, however, "government by laws" is not sufficient for a constitutional democracy — because it still begs the central question: What binds, or ought to govern, those laws? Who shall watch the watchman? This is the most fundamental question undergirding Rule of Law and Due Process of Law.
Is "law" anything the sovereign says it is? Is the "law-maker" merely whoever has a monopoly of coercive power? Is law (as Mao said) whatever comes out of the barrel of a gun? Does the U.S. Constitution ordain that the Vice President shall preside over his own impeachment trial in the Senate? Or is law, properly understood, itself governed by basic norms of law-making?
And, if so, what are those norms? Do they include such "unenumerated" rights, privileges, immunities, and entitlements, etc., as the presumption of innocence? May judges sit in judgment of themselves? What "core values" undergird enumerated and unenumerated rights, etc?
Can a parliament's legislation be unlawful? Can a constitutional provision be "unconstitutional" in the sense that it violates fundamental global norms of constitution-making which are themselves premised on that "presumption of Ordered Liberty" to which the Rule of Law is itself subordinate? The answer, since the Nuremberg trials following World War II, is — or ought to be — very clear. Yes. Some "laws" are lawless, and to obey them is a crime.
Under Hitler, the German Rechtsstaat was (at its very best) merely a Gesetzesstaat — a state that rules by laws — and that turned out to be very bad indeed. Since the Nazi era, German jurisprudence has rightly sought to define the Rechtsstaat as a "law-based state" in which "law" is itself "based" on principles that cannot be defied by anyone or anything, including the parliament and (perhaps) the German constitution or (as it is called) Basic Law.
The theory that law is whatever the ruler says it is was very popular, worldwide, prior to the rise of Stalin and Hitler. That theory is called legal positivism. Following World War II, the world increasingly abandoned legal positivism, but it remained central to Soviet law and remains imbedded in post-Soviet law. See Theory of State and Law. See also Lustration in Transitional-Justice Context.
A pre-war critic of legal positivism, and one of the leading philosophers of law during the past century, was the late Lon L. Fuller, a professor at Harvard Law School. His book, The Morality of Law (1964, rev. ed. 1969), sought to articulate the "unarticulated major premises" underlying the Rule of Law. The "unarticulated and even unarticulable major premises" he sometimes added, as I recall.
The following discussion is based largely on Fuller's work. A further discussion of Fuller's work and these "Ten Principles" appears in The Enterprise of Integrative Jurisprudence.