I've been told that is a seal brown. Black with brown points around the nose and flank are seal brown. This is my friends Seal Brown mare.
I don't think I have ever seen a true 'Dark Bay' I think its just another term for the seal brown. But for Blood Bay, now that is your picture perfect bay. Brown/red coat with black mane/tail/legs/nose.
I would have thought Seal brown, as well. I also thought there was no plum "brown" in horses, outside of misconceptions? (I mean I've heard people call chestnuts 'brown.')
We do have one Dark Bay, Darla, who is registered... Jack looks nothing like her, aside from the muzzle. (A picture of her is below, in her summer coat.) Jack isn't registered and is the run-of-the mill "mutt" (as far as we know), so it's hard telling and all a matter of judgement.
I told the girl who said he was a blood bay that it didn't sound right to me. I thought "blood" bay was more... bloodish-colored. Lol! I'd also seen pictures of Seal brown horses and figured, "Hey, that is so Jack."
But, in the same respects, I'm still very new to the equestrian world, leaving plenty of room for being wrong about things. (Shrug)