I'm talking about the definitions in regard to using the chess analyzer of course...

Obviously a blunder is the worst, mistake is the 2nd worst, and inaccuracy is the 3rd worst... but how does the analyzer classify which one is which?

Does it depend on the point differential that results?

I am not sure, but I guess it works like this:

Best move = 1.0
Inaccuracy = 0.7-0.8
Mistake = 0.5-0.8
Blunder = Anything below

Sorry bad at explaining. The software rates the position and depending on how much it worsens after your move, it gets either ?!, ?, ??

So an inaccuracy is always a mistake.

Yeah last I checked it's more like,
blunder,
then mistake,
then inaccuracy.

Thibault posted the official score difference bases for distinguishing them, but he's mostly just finding random terms to use, as well as hoping some English expert will correct him with better word choices so that he can improve them.

But mathematically speaking it's that simple.

So a mistake is always an inaccuracy, and a blunder is always a mistake (and an inaccuracy).

It's not a perfected annotation system, but it's had improvements.