Lol the term gets thrown around so much by marketing/advertising, it doesn't really mean anything. Another examples of such words often misused to hype up a pair of headphones are: studio-quality, monitoring, or reference-grade. Lots of headphones get advertised as such, but not really like that. So in the context of reading that word on the box of a pair headphones... it doesn't mean anything. Basically often used as a synonym for "hi-fidelity."
The "audiophile-criteria" usually is referring to how accurately the headphones produce the sound from the source. So that means a flat/balanced/neutral frequency response curve (without any coloration/bass-boost/v-shaped sound sig/recessed mids/that kind of jazz). What you hear should be the same as what the source file: a realistic, unaltered, natural portrayal of the recording. So additionally, it can include other positive sound quality attributes such as having high detail retrieval, transparency, clarity, resolution, speed, sound stage, texture... blah blah blah...
The ATH-M50 are often referred to as audiophile headphones, but they actually have a v-shaped sound signature with slightly recessed mids & emphasized bass. So basically, the word seems to have become meaningless. But if you read someone here talking about audiophile sound, it should be assumed that they are talking about flat sound signature with high sound quality attributes.
hahaha
Actually, your first paragraph doesn't make a lot of sense, especially when you do a pretty good job of describing in the second paragraph what audiophile headphones are. Adding "blah blah blah" at the end doesn't change anything either.
I will add that audiophile gear isn't necessarily about the flattest response but about most closely re-creating the sound of unamplified instruments (classical music, jazz, etc), as they provide a natural and relatively objective reference point. Some people feel that a flat FR is the best way to achieve this, others feel that some colorations (e.g., more prominent mids, warmer highs, etc) are preferable - regardless, the goal is to reproduce the original sound as closely as possible.
Now, I do agree that people use that term willy-nilly, especially here of Head-Fi, where rampant love of almost everything except Beats reigns supreme, and heaven forbid something ever get called out as being less-than-stellar in one of the many "Appreciation Threads". That doesn't make the definition meaningless - it merely requires the reader to take all the greatgreatgreat posts with a grain of salt.
The V-Moda M80 are fun headphones. They have punchy high bass and lively treble. However, they definitely do NOT do as good a job of reproducing the timbre, tonality and body of live instruments. They are good headphones for the price/intended usage, as are the ATH-M50s, but calling either of them audiophile-grade headphones is a joke - as I said, I own the M80s and am happy cranking some house/EDM on them, but when i am focusing on the music, they never come on.
On the other hand, the humble HD518s, at $120 or so, do a much better job of making a violin sound like a violin or a trumpet sound like a trumpet. Hell, even listening to well-recorded rock (Kinks, The Doors, Floyd), the HD518s are on a different level altogether. Yes, you are right, one is closed-ear portable while the other is a open-ear full-size but we were talking pure sound quality. And then once you get to the HD600/650s, you have headphones that still hold their own against megabuck headphones. If you want to get into closed headphones, I think the Momentums are better headphones than the M80s.
I actually agree that it is silly to argue about whether one brand is better than another based on specific models, esp with different sound preferences. However, V-Moda only has 2 models with some kind of hi-fi aspirations, the M80 and M100 and neither of them is particularly hi-fi (and I am not saying that is a bad thing - I am sure a lot of people will like the M80 sound to that of the 518 or Momentums), so in this particular case, one can actually make a comparison.
As such, in the context of audiophile speakers - in my opinion, at least, there is no comparison between the 2 brands if it comes to accuracy of the sound, when using live, unamplified instruments/vocals as the reference.
There is no reason for this to degenerate into a flame-war either. It is ok for people to disagree and state their preferences. If all we have are cheerleaders, then that doesn't help anyone.