Yeah, lots of games distinguish evading and missing.
BoF4, comes to mind, where miss via Evading says "Parry" and for missing via accuracy (see Ershin's physical, many of Ursula's attacks, Risky Shot/Blow, etc.) it says "Miss."
BoF3, it says "Miss" for both instances, and at first, I was going to correct Elfboy...until I remembered that I THINK Evading shows the character strafe a little to the the side, while Missing, they're stationary.
FFT (mostly applies to stuff like Breaks which aren't 100% Base accuracy), I believe it Evading it says "Guard" combined with showing a shield or them strafing to the side a bit (holding their arms up), or blocking with their weapon, whatever, while Miss it just says "Miss" (whether there's animation involved or not, wanna say it depends on the attack.)
Or what about ARPGs, where misses can just be totally out of bad aiming, and evading happens if you do connect, but the enemy actually manages to avoid?
The point is, bad Accuracy is different from Good Evasion. They yield the same result (attack doesn't connect), sure...
But well, lets look at an example!
In the case of, say, 50% accuracy, the attack will only hit 50% of the time. Unless you find a rare case where a game actually has NEGATIVE EVADE (FE4 anyone <.<?), that 50% accuracy can never hit more than one out of every 2 shots. Even if it ignores Evade, its still got a cap of 50% accuracy (Barring weird quirks of the system like Zodiac Affinities or Weapon Triangle Advantage that can alter rates one way or another, for entirely different reasons). See FFT Snipe where it ignores Evasion, but it has a base accuracy that is significantly below 100%. No matter HOW bad at evasion you are, these attacks can only hit 50% of the time, regardless.
By your logic, a character with "Below Average Evade" is suddenly allowing this attack to do something that it normally shouldn't, that being have a higher Hit Rate than is actually possible by the attacks distinctions, just cause the enemy has "below average evade" which in his OWN HOME GAME translates to a value well above 0?
Now, other side of the coin...
Say you have 50% evasion. Lets assume this is actually 50%, and not a weird FE style subtraction evasion which requires scaling (hence why FE is taken against hit rates above 100, etc.) So if someone has "average" accuracy which is 100% vs. 0% evasion, lets say (what many people claim is "average"; this is purely for sake of argument, mind, not saying I personally believe this), that attack will miss 50% of the time.
*HOWEVER*, lets say they come up against someone whose average effective accuracy is 150%. This means that this 50% evasion is suddenly 25% in practice due to 50% of 150% is still 75%.
Which is to say nothing of 200% accuracy which completely overwhelms that 50%.
Now, yes, there are evade rates that ignore accuracy. FF6's Interceptor comes to mind; he's a flat out 50% chance to block any SUCCESSFUL physical dealt to Shadow. Even if the move IGNORES EVADE, if its a certain kind of attack (basically Fight/Battle commands and Specials), Interceptor has a flat out 50% chance to block it.
However, these moves are no different than moves that Ignore Evade but have below 100% accuracy like FFT's Snipe.
Ignoring those exceptions, in any event, do you see the difference?
In the case of 50% evasion, it *CAN* be overwhelmed, and made to look worse than it really is, if you have good accuracy. If nothing else, refer to FFX. Wakka has no problems hitting those pesky evasive fliers that other characters struggle to hit. These enemies have great evasion, but despite this, cause Wakka's accuracy is so high, he can overcome it and still hit them with no problem.
Bad Accuracy, meanwhile, cannot overcome bad evasion. Momo's 70% accuracy in game stands out and she never hits anything more than 70% of the time on average. Even enemies with absolutely no evade, she'll still miss. The only way to get that 70% Accuracy higher is to either use moves like Shadow Walk which insure that the attack will hit, or give her accuracy boosters like the Artemis Cap. Either way, Momo's accuracy caps at 70%, and it cannot be increased higher than 70% based on what she's targeting alone (barring very bizarre circumstances, like as I notd before, FE4 PCs who can actually have negative evade.)
So yeah, while the result might be the same, and the two are often related, there's a difference between Evading and Missing, and as such, we can derive that there's a huge difference between 100% Accuracy and 0% Evasion, in that the former insures you'll always hit, while the latter means the enemy gets no hit penalties against you.
Its a similar line of thought as how 0 Defense =/= 0 Defense. Phantasy Star 4 enemies, for example, have such horrid defense that Profound Darkness' "low" defense score of 0 goes completely unnoticed, and is "low" in a pure numerical sense, when in practice, it means a whole extra like 2% more damage.