There is no legal distinction.
Using legality as a gauge for morality is not always the best thing to do, especially when these are law enforcement agencies operating entirely within the law.
no where are barbwire or “razorwire” considered a “booby trap.”
So you're being wilfully obtuse. Nowhere was anyone implying the use of barbed wire is what makes it a booby trap. Every single time it was mentioned, it was clear: it is a booby trap because it is a purposefully hidden device meant to cause harm to those who stumble upon it by accident.
It also does matter the distinction between razor wire and barbed wire. Barbed wire you can hold in your hand. You can grip it, move your hand along it, and indeed are unlikely to be very harmed by encountering it; it is designed as an unpleasant deterrant, not a dangerous one. Razorwire, on the other hand, is designed to cause harm: every part of it is dangerous, and an encounter with it would result in deep lacerations.
But again, it could be barbed wire and my point would stand: the concealment of it is what makes it a booby trap, and what makes it a problem.