It’s called Constitutional Carry for a reason.
If it’s good enough for Vermont, it’s good enough for Texas.
While the name “Constitutional Carry” is probably the best term because it’s better understood, I think the more accurate name would be “Natural Law Carry”, as this right was not created by, but rather acknowledged by the Constitution.
Note when referring to this right the 2nd Amendment does not say citizens “shall have” the right, but rather simply refers to it as “the right”, without there being any other part of the Constitution that had already established that right, which therefore means, to me, that they are referring to a right that was established by Natural Law, as opposed to, say, the right to a trial by jury, which is established by the Constitution.