Basically, all of the first hand silkworms available here are in general 4 way hybrids. (sometimes 2 or 3 , but mostly 4). They are bred for commercial purposes, for recreational and for hardiness. Most of the ones here are mixed in with a multivoltine line from a warmer climate area. We all know silkworms originated in Asia, but now we have European lines. I don't know how they go about claiming a line is specifically European, but I guess if a line remains phenotypically the same and produce predictable generations for many many years, it can be recognized as standard.
Back to the question, there are no pure lines available, except those that are safely guarded in research institutions. You can obtain pure lines only in writing, and through exchange programs. Or a student obtains eggs and smuggles them out :)
When I started working with the silkworms in this country. ( I am not a researcher, just an enthusiast) I thought I wanted to isolate some of these desired traits from these every day silkworms. Specifically I wanted to separate out the white seductress from the masked face for the reasons that white seductress made a better canvass for coloring. But as I bred down the lines, despite the appearance of the chosen breeders, I ended up back breeding them, splitting up to the lines of the top origination. This is why you end up with a variety. You can back breed, but I read that it will take you about 30 generations to get some uniformity, but not consistency. In simple classification, P1 stands for first parent, and F1 are for first gen hybrids.
The best breed that I enjoy working with are definitely the tiger silks. ( I think I should really call them Tiger hybrids now). When you breed them, you will notice they are not all consistently the same darkness. But those are usually culled, or fed off, and you would use only the darkest ones as your breeders. Keep working down the line, or rather UP the line to get them to have that gorgeous velvety skin. They do spin gold silk, but are coarse and small cocooned. In general, color silkworms are hardier but smaller in size, reaching only 2 inches and lay smaller eggs.
There are cocoons that are peanut sized, round, or oval. The largest I have seen is a man's large toe size ( those silks are meant for silk duvets- imagine that!) and the smallest I've seen is the size my pinkie.
There is a lot more in this area. But this will do for now.