Now that the bush I planted (that came as a 'Dr. Grill' but is supposed to be 'W.R. Smith' and the same as "Amelia Anderson") has flowered, I'm quite confident in saying that my Dr. Grill from Honeysuckle is definitely not William R.Smith. I posted a couple of flowers of W. R Smith, and they could very simply be described as creamy white (no real hints of pink at this stage). Their fragrance to me is like a weaker Maman Cochet scent, the petals are rather thick and waxy. The biggest difference so far is in the habit of the bushes and the leaves. My Dr.Grill has larger leaves with a more undulating edge; the growth of W R Smith is more classic Hybrid Tea like - straighter, more open, erect growth - whereas the my Dr. Grill's branches are a bit more sinuous, and they get sent up from seemingly anywhere on the bush so it creates a denser more Tea-like habit. Also, the flower stems on W.R.Smith have tended to remain reddish when the flowers open, whereas on my Dr. Grill they have changed to green at that point. W. R. Smith's unopened buds are squatter too.
I know I haven't had this new rose for long, and it's hard describing differences,and culture could come into play a bit, but I can tell simply by looking that they aren't the same.