Unique was, I believe, it's own powder, developed specifically as a new powder, not as the byproduct of yet another smokeless powder.
Bullseye was originally the fines from a rifle powder. Name started with an I... Dang, it was right on the tips of my fingers, and now I can't think of the name....
Infallible Shotgun Powder, which was incredibly popular in the early 1900s and was the first truly successful nitro smokeless shotgun powder, as opposed to nitrated pulp powders like Schultz White Powder, which was a nitrated wood pulp.
Bullseye proved to be popular enough that it made sense for Hercules to bring it out as its own powder. Also, if I'm not mistaken, Du Pont MAY have kept the Infallible brand for its own when they spun Hercules off.
I've seen a sample of Bullseye supposedly from a lot packaged in 1901, and it bore absolutely no resemblence to what we now know as Bullseye. Very irregular.
Frankford Arsenal used Bullseye powder to load standard military loads in the teens. I've seen boxes of military .45 ACP that list Bullseye powder specifically on the label.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.