@THEIS can probably best answer this question for you.
As you pointed out, specs are specs and there's not much wiggle room, if any at all.
Some items have to meet extremely stringent tolerances or worse, go through flight certification.
An example of the air/flight certification was the Purolator brand fuel cooling loop filter made for the B-1B. Back in 1987, that filter was $1608.00.
Crazy, right?
That filter had a Purolator part number on it that ended with a dash.
Purolator made another filter just like it without the suffix.
That filter was $53.00.
Was there any difference in them? According to Purolator, not at all, except for air certification and the suffix to the part number.
They even told us they would verify the performance was the same.
So, to answer your question, not always, but sometimes.
And now for a bit of humor, here's some military Beta binoculars for you.
Apparently, they're not good enough to be Alpha glass...