An old growth shaft, by the very definition of old growth, means that it was created using wood that was harvested from a 150+ year old tree. That's it. Nothing more, nothing less. It could be white or brown, heavy or light, tight grained or loose grained. It's subject to the individual tree's growing conditions and genetics.
Take two trees & plant them in different habitat. Put one in an open feild of bottom wetlands & rich soil. Put the other on the top of a stony, sandy soil hill with lots of rocks. Let them both live 150 years. The tree in the feild is going to be huge diameter with few grain lines per inch, a very white sapwood with very dark & large heartwood, and fairly dense wood. The other tree will be sandy tan in color, rediculous tight grain lines, small diameter, and likely will be lightweight with stringy weak grain. Both are old growth trees & shafts made from either is considered old growth shafts.
Now take a huge, dense & ancient forest and plant a tree in the shady side of a hill down near the bottom, ideally in a revine. Let it grow 150 years with minimal sunlight but lots of nutrition & moisture. This tree will grow straight up like a post and stay relatively slim diameter. The wood will have tight, uniform grain lines. It'll have lots of creamy white/yellowish sapwood with a small brown heart. This is ideal shaft wood. It'll be dense, hard, strong, & a very fine texture. It's also old growth like the two trees above, but is the old growth that is so sought after & revered by cuemakers.
Once cut to lumber, then cut into shaft squares & dowelled, how does anybody know what wood they are getting? There are endless variables. I have cut 300 year old trees that had 10 grains per inch. I have cut 2" diameter sapling trees that had 40 grain lines. Last winter I cut a tree that was 10"-12" diameter & it was around 180 years old. But how do you know what's what once it's a shaft? You don't unless you were there to see the log before it was milled. So whenever you buy & pay premium for old growth shafts, you may want to ask how the builder knows it's old growth and not just his speculation.
I'm not trying burst anybody's bubble but I see a lot of old growth shafts being sold lately & I don't know a lot of sawyers cutting old growth & when they do they don't market it as such because to them it's just another tree. I know which of my shafts are old growth because I cut the tree they come from in many cases. But the shafts I make from bought lumber, I never label as old growth because honestly I don't know. If the shaft has 20+ grains per inch, it's likely old growth because the tree has to be large enough to cut & if it has 20 gpi and large then it's an old tree. But again it's not a sure thing so it can't be accurately claimed.
Sorry for the long post. Hope it helps.