McDave said it pretty well. Here's another opinion.
Trad is a descriptive term, a real word, and is quite useful if we don't get carried away with a 'Hatfields and McCoys' mindset when applying it. Archers won't accept one meaning for it so all we can do is assign our own meaning. For me trad really is more about old-style hunting gear rather than target gear, and traditional hunting gear doesn't include items like bowsights, carbon arrows, electronic nocks, berger buttons, bows or add-ons that mimic compound setups, etc. Not that there's anything wrong with target bows or compounds but its hard to regard or label them as traditional gear. Thats not a condemnation, just a personal decision that I think many share. Basically, traditional is about a simpler approach without gadgets or things that are mostly used on the target range.
I think mixing the latest in target-style bows and arrows with the simpler old-style hunting bows and arrows is where most of the bad feelings come from in the archery forums. Very few folks would say that hi-tech target equipment isn't good for target shooting (duh), but lots of folks (including yours truly) simply don't care to equate that type of gear with the simpler designs. In effect it muddles the identity of what USED to be a fairly simple undertaking, both re gear and mindset.
With the new target-style technology fad we're morphing much closer to a compound bow kind of identity than a simpler-makes-sense identity. In that sense what we call our equipment and how we define and use it certainly does matter. Making a few basic decisions to clarify obvious differences in gear/styles is a logical step that for some reason makes some folks respond defensively with 'traditional elitist' namecalling...in a revengeful tone. Too bad we can't agree to accept something better than 'no wheels' as the one and only definition. Sure would make understanding what we do easier and save alot of bad feelings across the board.