Due process is a difficult thing to define, and the Supreme Court has not been much help over the years. Here's what we can say about due process: In the Magna Carta, due process is referred to as "law of the land" and "legal judgment of his peers." Some state constitutions continue to use these phrases.
The reference in the 5th Amendment applies only to the federal government and its courts and agencies. The reference in the 14th Amendment extends protection of due process to all state governments, agencies, and courts.
Due process, in the context of the United States, refers to how and why laws are enforced. It applies to all persons, citizen or alien, as well as to corporations.
In that, the "how" is procedural due process. Is a law too vague? Is it applied fairly to all? Does a law presume guilt? A vagrancy law might be declared too vague if the definition of a vagrant is not detailed enough. A law that makes wife beating illegal but permits husband beating might be declared to be an unfair application. A law must be clear, fair, and have a presumption of innocence to comply with procedural due process.
--- Even if an unreasonable law is passed and signed into law legally, substantive due process can make the law unconstitutional.
Someone accused of violating a legal prohibition in entitled to a hearing.