Server-side UI = You PC only sends input signals to the server and he evaluates it and triggers the action (even for stuff like inventory)
Client-side UI = Actions that are unrelated to the world trigger immediately and other actions are queued (inventory opens right away, maybe even items show if they are cached)
Thus far only character movement is client-side (which explains why other players see you far behind them while you say you're right behind them)

But that bit of lag is my least concern. More annoying is the fact that this lag is eating away actions and that UP and DOWN sometimes browse through the skill panes and sometimes switch through targets :/