There is no single, fully standardized way of grading briar. Very roughly you have primo, which is pretty ugly, Extra, which is nicer, and Extra Extra which is nicer yet. But what each mill or cutter means by such terms is not the same, and certain mills grade entirely outside of those (somewhat old fashioned) designations. Let's look at a few blocks.
In this first picture, you can see the strong, regular, tight grain in the block at left. Block on top is also tight and even, but the cut is not quite as good (from the top view, you can see the block is pretty crooked and the grain will follow that shape). The block on the right shows far less grain, it's a way less pretty block. And this is born out if we see the crust:
The crust or outside bit shows nothing but uniform tight tiny bumps on the best block. A little looser on the middle block (and you can see how crooked the grain runs), and the block on the right is wide open, big rolling lumps.
So that's probably two XX blocks and one X grade block under most schemes. Mimmo grades by number, with 1 being well cut dense XX and 2 being just a little less amazing. 3 is actually selected for blasting due to wider rings and lower physical density.
So when we look at a Peterson Rosslare, or a Sherlock series pipe, we see a lot of fine tight grain, hopefully none or very few little pits, and basically a nice even presentation.
I can offer basically no correlation between grain density, orientation, growth rings.... in terms of how a pipe smokes.