There is no "true" difference in that you can pretty much use either one for the other, I'll elaborate on that a bit later.
In most cases though, people will be refering to a specific setup for a ship.
Now, with mission/pve setup you're running a specific setup to counter the target rats, you do this by fitting your tank for their damage type, and being sure to do their weakest damage type as your offense.
For pvp it's a bit different, you must factor in different scenarios and uses/tactics for the ship's loadout, being sure to think of as many counters to things, drone types, any time of ewar(scram, web, damp, etc) and other things like tank. You have a disadvantage of not knowing the type of damage you'll take so you have to fill as many of the holes as possible.
There is also the other assumption.
They could mean "stereotype" wise, where a Raven is great for running missions for a fairly nice tank and being able to spew any of the damage types at the rats from afar, where as it blows in pvp due to lack of free mids/time the missiles travel. Something like a Megathron, which kinda sucks for pve, but is fairly nice in pvp as it can fit rails and hit a nice distance instantly or go close and tear stuff up. It's things like that that'll make people call the ships themselves pve/pvp ones, because they fail at one task, but excell at another.
ten there's the ships that kinda fail at both... and those are called amarr
*run away after throwing that line in for the heck of it*
Bout the mega being poor at pve.