As I said before, observation of grinder differences concludes in pointing out nuances of taste for given beans brewed after being ground on different grinders. I believe this is great observation but honestly, on its basis again it would be hard to tell anything about the grinders apart from one or another being perhaps better suited for some coffee and less for another, or that some notes of given coffees are lost on one and accentuated on another. After trying out many coffees for specific grinders comparison it would be possible to point out pluses and minuses of both. But that's quite practically impossible to do in real life!
But I did find (a bit accidentally) something else can be done!
It is actually to smell the grinder's differences!
How you practically do it?
For hand grinders you should smell the grinds while you're grinding them, you should sniff above the hopper, while opening it a bit. The grinder profile will pop up in your nose.
It may be difficult to point out from remote what we're searching to smell out, but if you have two different models of hand mills (really I mean two different brands, because in my case it is so that the mills I own are quite consistently in good shape) you can smell this way both of them and then if you notice the difference between them, then this is what makes the difference in taste - that is the difference in the mills taste profiles.
For electric grinders, you should remove the hopper and sniff right after you just stopped grinding. It is confirmed for Mazzers but I'm certain it will hold onto other brands as well.
This way of sniffing together with tasting the shots from the grinders is really giving away the grinder's profile, not just differences for certain coffees. I can't say if it tells the full picture, because I don't have possibility to compare my grinders to a grinder that is significantly inferior - I have the Mini and three working perfectly KyMs and a Mocca also working, though grinding on it for La Spaziale is at the border of its capability (it will never make a choke ) and a Zassenhaus which I didn't want to push (the Mocca has different bearing that makes it possible to push it to very tight settings while the Zass doesn't). I've come up with this after comparing among my mills family and a tiny bit outside. This is also how I came about with the grinders taste description (the smoothness/sharpness, depth/flatness and messiness/cleanness).
The differences showing up in this way of checking are all over the taste map, it shows the nuances in acids (these are most apparent at least to my nose), bitters, sweets, earthiness. I think the more experience the person doing the smelling has in tasting coffee, the more it will be able to tell.
For example my KyMs vs my Mazzer Mini taste smoother, a bit softer; more clean in higher acids but then loose on bitters and Mazzer gives fuller sweetness while being less clear in the higher notes and sharp. But it has advantage in the sweets (vs another electric) with being deeper-cut and not rounded-cut.
Then my Mocca vs my KyMs taste deeper overall, and its profile is more balanced, yet again the bitters are a bit less visible then in Mazzer while the rest stands as deeper too, though a bit lacking in body (it is logical - deeper in a sense means more 'inner space' of taste, then the body may easily be lacking if it is not cared specifically in the design). (But with all this depth of this Mocca's taste - it takes over 200 turn to grind a double...

) Then the KyM's body vs Mazzer's is drier in taste - in smell it is a bit shallow.
So this is what I wanted to share. I will be happy to hear others experience - please try this out and speak, most of you have more possibility because you have access to more equipment easily!