Online PC gaming on wireless connection

Hello.

Just for a bit of background information, I once had a really crazy internet connection. I used to run an ethernet cable from my computer to another computer that was connected wirelessly to a neighbor's router. When I did this, I noticed that in online gaming, I would be seeing ghosts of other players about a second or two after they'd moved around. For example, when playing Counter Strike Source, I would attempt to follow someone running around with my crosshairs, attempting to keep my aim focused on that person at all times. When I did this, to me, my aim seemed perfectly normal, and I could focus on the other player, no problem. But when someone else viewed my screen, they could see that I was in fact aiming at a "ghost" of the player, about a second after they'd already moved.

At this time, I'm running a wireless USB adapter and I'm connecting to a router that's in my house. The difference being that directly connected wirelessly to the router, without the other computer. I've been having a really hard time playing lately, and I'm wondering if I could be experiencing the same issue due to not being plugged directly into the router. Is there any validity in that?

TL; DR: Does online gaming with a wireless connection make me see everything happen a second after it happens?