Heres my thoughts…
Hand dyed means the color was applied manually rather than in bulk by machines. Any times this is done by dipping the whole hank or just sections of the yarn in pots containing the dye. To me it also means I should expect the dye lots will be in smaller batches, but I may be able to get more than one hank that will match.
Hand painted is where a device-(squirt bottle, brush, sponge etc is used to paint individual strands or sections of yarn. I expect hand painted yarns to vary between each hank of yarn.
Self striping has long runs of each color so that when its knit up in the recommended gauge you get stripes of that color.
Varigated means that there are differnt colors in the yarn but they are not necessarily meant to produce a pattern inthe finished product. Of course they can, but they don’t have to as opposed to self striping which you assume (in a perfect world) will produce stripes.
Also, I was reading an article referring to spinning and how you can create a sheen or luster on yarn by spinning wet. Now, being a VERY new spinner I wouldn’t know but I imagine it helps the fibers stay “tucked in” as they are being spun there by eliminating halo and encouraging the fibers to all lay flat in one direction.
Having said all that, we live relatively close together and I know Kiparoo Farm has a yarn they market as Luster Spun.
Hope this makes sense!!!