Though the intracacies of the manufacturing process are interesting, as a practical matter, the objective parameters you as a consumer have available to inform your decision are the arrow's advertised straightness tolerance, weight tolerance, and dimensions (inside/outside diameter). Other than those three parameters, everything used to describe a particular arrow is mostly marketing fluff (e.g., "high modulus carbon," "premium carbon," "dual spine weight forward," "hard-hitting jackhammer guaranteed to punch through an elephant scapula").
Spine tolerance is arguably as/more important than straightness and weight tolerance, but Black Eagle is the only manufacturer I'm aware of that makes any numerical claim about spine tolerance. Most manufacturers claim (without numerical context) that their arrows are "spine grouped/sorted" or "spine aligned," but only BE actually puts a number to their spine consistency (
±0.010" deviation across a dozen arrows).
Most arrow models are offered in multiple straightness tolerances (often ±0.001", ±0.003" and ±0.006") with price increasing as straightness improves. The straighter the better, but what you truly "need" is debatable and relative to your individual shooting ability.
I don't pay any attention to the advertised weight tolerance of the shaft. They're all good enough that it's not going to appreciably affect the finished arrow. Consistency of total arrow weight can be tweaked by weight-sorting other components when assembling the arrows.
I believe that a smaller diameter arrow with thicker wall tends to be more durable than a larger diameter arrow with thinner wall. But I've never seen any actual data from destructive testing (e.g., ultimate bending/shear/compression/impact strengths), so this belief is just based on a combination of engineering intuition and anecdotal experience.