Match components are "supposed" to have tighter tolerances, but for 99% of shooters they'll never notice any difference downrange.
Tighter tolerances based on what specifications is the question.
Yes you should expect that a primer or loaded ammo that says "Match Grade" (or something similar) on it should mean that manufacturer either makes that item with a process that uses tighter tolerances (i.e. less variation from one to the next) or that they sort the output of their standard process and package the resulting pieces that fit the tighter tolerance separately from the rest.
However, I don't think there is any accepted third party definition of exactly what those higher standards or tighter tolerances should be - and even one manufacturer to another might have different definitions of what it means to have a higher tolerance.
The idea being that the less variation there is from round to round in every parameter that can be controlled should translate into less variation in the hits on the target - of course there are many variables outside of the round itself whenever you shoot - target or match grade should simply remove the ammunition itself as a variable.
In other spaces - such as automotive - higher grades might mean brake pads that wear longer - or a flywheel that is more finely balanced. Makes me wonder if anyone out there is advertising (for hand loading or as complete ammo) projectiles that are harmonically balanced so they spin perfectly. Its one thing to have a set of projectiles all with the same weight - but if they are not also the same shape aerodynamically and evenly balanced etc they might "fly" differently. Even a small difference in hardness that affects contact with the rifling will have an effect.
You could likely fill a couple pages with all the potentially variables. Some of which are going to have tiny effects and some of which are going to have large effects on the outcome of a shot fired. Some of which will have inexpensive ways to improve and some will have very expensive ways to improve.
In the end it depends on what you are trying to accomplish.
For a primer it could be as simple as the recipe used provides a more reliable or consistent ignition - or it could be as simple as an individual inspection to ensure that not a single "bad" primer makes it into the box (by "bad" I am thinking primers with no anvil or the wrong amount of explosive might have slipped through the automated process but is excluded from the "match grade" package, which would mean there is no difference at all in the construction or formulation just extra checks for defects).
