For me ...
If it has a straight stock and a round barrel, it is a Texan.
If it has a straight stock and an octagonal barrel, it is a Cowboy.
I think all the "old" rifles were just marketed as a round or octagonal barrel as the buyer desired. The terms "Cowboy" and "Texan" are just later marketing gimmicks.
The heart of the wise inclines to the right, but the heart of the fool to the left. - Solomon