You can't just brush it aside as some quibble about definitions. It's a fundamentally substantive difference in the two structures: one of these has an indisputable source of truth (a foundation everyone can witness) that everything else is built on top of -- however shakily! -- and the other does not. Regardless of whether you include the upper parts of this metaphorical building in your definitions or not, the foundations are not the same.
Yes, it is a substantive difference but it does not follow that this difference provides the 'constitution' property.
> one of these has an indisputable source of truth... the foundations are not the same
They are so similar as to be almost the same and if an 'indisputable source of truth' exists anywhere, it is not in the written documents or their structure but unwritten norms and rituals sit beneath both.
What stops a President from simply choosing to ignore a Supreme Court ruling and what prevents the King from returning to personal rule?
The lack of arbitrary rule is a defining feature of both and relies on something that emerged rather than something imposed from without by written words.
Legally? The fact that everybody under the president -- including those in the military -- understand they are swearing their oath to the constitution -- not the King, not the Crown, not God, not the Supreme Court, not anything else. And that the Supreme Court says what the constitution means. And that if there is a clear and direct contradiction between the Supreme Court and the president, the former trumps (no pun intended) the latter.
Physically? "Nothing", yeah. Same goes for non-presidents. If you can get enough people to follow you (or maybe at least enough of the people with guns) everything else becomes irrelevant, including whether your title was president or King or God or Constitution or whatever.
> The lack of arbitrary rule is a defining feature of both
It is emphatically not. There are lots of countries with constitutions that nevertheless have arbitrary rule. As there are countries without constitutions or arbitrary rule.
> They are so similar as to be almost the same and if an 'indisputable source of truth' exists anywhere, it is not in the written documents or their structure but unwritten norms and rituals sit beneath both.
No, that's exactly what those are not. Unwritten stories, traditions, and rituals are very much disputable. That's kind of the entire point of writing things down, and the point of the game we call Telephone. The indisputable bits are physical artifacts everyone can see with their own eyes.