Just to clarify what "running" actually is.

The problem is that what started as a specific term for "running a set route as quickly as possible" has with time become a generalized term for "someone else performing the taks instead of you".

You do know that language evolves. Incorrect one year can become correct the next. Dictionaries monitor current usage and change definitions accordingly.

Running = letting other player(s) leech while you do the job for them, it can be running to outposts, finishing elite missions (uw, doa, etc), finishing vanquish, normal missions, or anything else.
I'm sorry that you have to hear this but believe it or not, words sometimes change their meaning on the internet. Shocking, I know.

in MMO's (yes, also GW) we mostly use "running a mission" instead of "rushing a mission"

i dont see the point of a discussion, but dont get angry everytime you see someone asking for a mission/quest/etc RUN, instead of RUSH

thing is (also say that when someone is annoyed by someone else's bad english), as long as you understand what someone means, there should be no problem, and if you make a problem out of any small thing, your life may be hell at times, to avoid heartattacks or anything, just try to ignore such behaviour, and join the community

Those terms are pretty different if you want to be a linguistic purist [hi OP].
As described earlier, 'rushing' values the speed, while 'running' focuses on getting the task done.
If someone pays me to run mission X for them and goes AFK, and i don't really want to rush it in five minutes but take my time to visit all the chests, kill some mobs and so on, i am still running them. Thus i am a runner - getting the mission done for payment - but not a rusher. That's the main source of this distinction, with clear division between the two.
Thus, actually, those who run past the monsters only to complete their goals as fast as possible (including getting to another outpost) are better described as rushers, not runners. As odd as it may sound, it's the only sane way because there's no other term widely used within the community that might distinguish 'those who just run others' and 'those who complete stuff for others'.
The OP would be quite right IF there was a commonly used third term (not talking about ferries right now), describing either 'those who only run to places' or 'those who get tasks done'. The postulated "lf vanquisher for x" or "lf someone who would do mission x for me" is not correct, taking the simplification of the used language into account.

Exactly! Just as "noob" evolved from the word "newbie" and meant the same thing and later became a derogatory term for an experienced player that is bad at the game (while also maintaining the original definition of "new player").

The English language has countless words with multiple meanings.

Do you laugh out loud every time you say "lol"?
Same thing.

I don't know if the OP is actually a genius with getting so many bites or if they just have issues taking something so petty to this level.

P.S Nice touch though saying your trying to educate the people that want to be educated must feel like your godly. THE END and good luck.

Common usage changes the meaning of words.