Stand still or move around (PVE)

I decided to start leveling a warrior on the new froustmourne server, I haven’t levelled one since moltenwow and honestly barely remember the experience.

I decided to level as arms and am currently in my 60’s. For the entire leveling experience, I have been using left/right mouse button to move around the mob while attacking and waiting for procs. I think this is likely because I watched a couple PvP videos and thought this was the way to play the class.

So, stand still or keep moving around during PVE? Is anything gained/lost either way?

Generally speaking, standing still will terminate the chance of you moving away and not doing an auto attack on time which could result in some small DPS loss.

It depends on what type of mobs you're against.
In general, just stand still. But if you're against a mob that hits fast, you can use kiting as a way to be defensive. The more range you have, the less they can hit, while you wait for your next auto-attack.
PVP wise, you always want to try and be behind the enemy, so that they have less chance of dodging/parrying/blocking your attacks, which significantly reduces your damage output.

It makes almost 0 difference. PVE mobs are always facing you, you can't trick mobs to get that "Target must be in front of you!" error so they'll still always hit you if you're just moving in circles. You can kite them a bit (slow them, run, wait for swing timer, go hit them once, and run again) but that will most likely cause you to have less hits since you can't time it perfectly. You're more likely to do more harm to yourself than have some benefits.
PVP yes, standing behind is a good tactic since some (most of them actually) spells and attacks require the target to be in front of the player.

Main reason why you want to move as little as possible in PVE has nothing to do with you, but with your party/raid. Everyone makes at least a bit more dps when they can stand still. You want to group mobs close to each other so they are easy and efficient to AOE, you should move in quick bursts when necessary and possible. With bosses its also important how do you turn them - attacks from behind are less often parried (require less expertise).

Position and turn mobs/bosses so every meele can stand behind (back leg side for dragons) and out of abilities on the ground, while moving as little as possible.