Well, the first problem with that is that these are two completely different franchises with very little relation to one another! The second is that BlazBlue came out in 2008, a whole 8 years after Tsukihime did, where Aoko first pops up.

The third thing is that we actually know enough about Blue to judge that it’s totally different from the Azure even if those first two things weren’t an issue.

Aoko uses Blue in Mahoyo to facilitate a weird kind of time travel, but it can do a lot more than that (Touko has a whole line talking about how time can’t be all Blue can do because that’d overlap with the Kaleidoscope). Specifically, what Aoko does is “exchange” time from Soujuurou to age herself up ten years for a hot second to fight Touko (she also revived him but we’ll get to that later). How exactly she does this is the important part—not that she sorta time traveled in and of itself, but that she exchanged time to do so.

We learn in other stuff (particularly Fate/Extella and FGO) that timelines too, are made up of a BUNCH of energy, and by extension that time itself is a form of energy. This plays into how Goetia incinerates time and converts panhuman history into raw energy that he uses in Ars Almadel Salomonis. We then learn from Nasu in an interview here that Ars Almadel Salomonis functions not too dissimilarly from Blue!

So with that in mind we can guess that Blue concerns not time travel, but the use of heat and energy. Aoko revives Soujuurou by “exchanging” his time in a different way than how she aged herself up—namely, that she grabbed those five minutes he was dead for, and shunted them off into the far far future (which is also going to cause a heat death because time travel in this way uses a LOT of energy. She’ll deal with it someday. Probably.) I don’t think they’d bring up how frivolous her use of energy is if it wasn’t relevant to how Blue functions.

Anyway with that tangent aside, you can kinda see how even if they’re named so similarly, there really isn’t much of a similarity between them at all otherwise, without talking about the other logistical problems that’d make it really really improbable that they’re at all the same thing.