I think I have more of a European (civil law?) conception of "rule of law", centered on the law itself: it must be clearly written, it must apply equally to everyone, etc.

Americans seem to use the term for something that should more properly be called "rule of magistrates". Judges can order pretty much whatever they want (unless overruled by a higher judge); prosecutors can charge or not charge different people for the same crime at their discretion; the Supreme Court just grabbed the power to decide what is constitutional, which the constitution nowhere grants it; etc.