With most HT's the climbing version is a sport, as you suggest.
I believe you will find that David Austin discovered some time ago that certain of his roses can grow really big here in the US compared to the British Isles. And he decided to create a line of climbers by simply training the same roses, using a smaller number of canes than would be used for a shrub. I've read a lot about DA roses, and nowhere is it suggested that the roses marketed as climbers are sports of the originals.
Of course, some of his climbers such as Generous Gardener, Malvern Hills, etc. are actually real climbers. Abe Darby, on the other hand, is on the cusp. One parent is a climber, the other is a big shrub. It can reasonably be treated either way.