Player to server connections better?

(it's been a while since I posted)

I'm not a very computer literate guy, so I'm not sure if there's a proper term for this. But, me and my friend were debating about what kind of connections (possibly wrong term) are better when it comes to online gaming.

And I was wondering about...

Are the connections we make, connect from player-to-player directly, or do we go through the server first? And which one is better in terms of lag and such?

I'm talking about room-based (party-based) mmo games where you go to a separate room from the 'world' like DFO, Grand Chase, Lunia Online, etc. but mainly DFO.