It is generally accepted to be, bluegirl. It's very easy for many roses to look like Slater's Crimson China because there are so many DIFFERENT Slater's Crimson Chinas. Very often, it was distributed as seeds. Self seedlings often resemble the parent and each other very closely, but not perfectly. You find the same variation in species, due to the wide variations possible in many species as well as to their also being distributed as seed. Kim

The "Caldwell Pink" and 'Pink Pet' situation is odd -- They are surely the same rose, in that they grow and flower identically, although I'm not aware that anyone has actually tested their DNA (we should do that). HOWEVER, what we can be quite sure of is that the correct, historical name cannot be 'Pink Pet', which was a China, and this rose has little in common with a China, other than its quick repeat bloom. The leaves, prickles, flowers, etc., are all wrong for a China. Rather, it appears to be a repeat-flowering R. setigera hybrid, maybe with some Polyantha in its background. So at least with "Caldwell Pink" there is truth in advertising, in that the name indicates that we don't know its historic identity. 'Pink Pet' was given to the rose, I believe by Florida rosarians, to have a "legal" name under which to show it in ARS-sanctioned rose shows. In any case, there is no direct, proven (nor even suggested) link between this rose and the original 'Pink Pet'.

Ah, interesting--thanks to you both. I hadn't reckoned on the variability of seed-raised plants, but it's so obvious now.
As a matter of fact, My "Martha Gonzales" (from ARE) looks like SEVERAL named Chinas. And it is quite different from a "Martha Gonzales" I had from Chamblees. ARE's plant is tall & vigorous with big, open, white-centered fragrant flowers. The Chamblee's plant was petite in growth habit & it had more delicate, folded flowers with only a light scent

And I have NEVER been able to tell the difference between my Cramoisi S. & Archduke Chas, both from ARE.