Ultrachrome was the original pigment ink for the 2100/2200, and as Richard said, had K and LK but no LLK.
Ultrachrome K3 was for the 2400 / 3800 and added LLK. I suspect that the other inks were the same as Ultrachrome (K2) but I have no proof of this.
Ultrachrome K3 Vivid was released for the 2880 / 3880. My understanding is that with the exception of Vivid Magenta and Vivid Light Magenta, the other inks were the same. This is strongly implied by the fact that you could use 3800 carts in the 3880, other than VM & VLM.
Ultrachrome HDR was for the ten ink printers and added orange and green. I assume that the other inks were the same as Ultrachrome K3 Vivid, but again I have no proof. Based on what I've read, the additional two inks were of little benefit for photography and were intended for graphic arts printing.
UltraChrome HD pigment ink is intended for the SureColor printers like the P600 and P800, so the naming is potentially confusing, given that there's also HDR. HDX is the version of HD for the ten ink printers. We have to assume that the blacks are quite different to Ultrachrome K3 Vivid, but it's not clear whether the other inks have changed. I read one report of someone who was sent a refurb 3880 (I think) and one of the included carts was for the P800 (cyan I think). When he queried this, he was told that it was the same. This surprises me, given the difficulty that Jon Cone has reported getting refillables for the P800, but there was no follow-up report about whether the P800 cart really did work in the 3880. There are also reports that yellow has been reformulated for longevity, which if true would be no bad thing.
This reads like a claim that there have not been all that many changes to the inks since the 2100/2200. The only ones that I've seen Epson promote specifically are the introduction of LLK, then VM and VLM and now the blacks in the new HD inkset. It's possible that there have been other subtle reformulations along the way, but if so then subtle would be the operative term. I'm happy to stand corrected if I've missed anything.
I guess it's possible that you could damage a print head by using newer ink in and older printer, but personally I think that's unlikely. After all, people use pigment inks in a 1430, which is a printer for dye inks.