There were disagreements about the meaning of the “Due Process” clause at the time it was adopted, and there are disagreements about its meaning today. But the disagreements we have today are not the same as the ones that existed back then. Two hundred years ago, legal minds disagreed whether the clause should be read narrowly (referring only to the necessity to adhere to certain judicial proceedings, such as the ones named in our Bill of Rights) or whether it should be read more broadly (referring to the necessity that judges and police must always act according to the law, whether that law is found in the Constitution, the common law, or regular legislative statutes). But in either case, it was a restriction on the courts and executive branch only, not an independent restriction on the legislature.
Procedural Due Process is a narrower reading of the Due Process Clause, while Substantive Due Process is newer and even more broad. According to this interpretation, not only the courts and the executive branch, but even the legislative branch is constrained by the “due process” clause. The “substantive due process” approach considers some rights as so fundamental that the government cannot take them away no matter what procedures it uses. This interpretation of the “due process” clause has been made even more significant because of its reiteration in the 14th Amendment, which means that state governments are restricted no less than the federal government. People may disagree about the meaning of the “due process” clause, but no one doubts its significance.