A picture worth a thousand words
The item is called play and charge kit and it's available as a separate itemhttp://www.xbox.com/en-US/Xbox360/Acces ... ychargekit
or as a bundlehttp://www.xbox.com/en-US/Xbox360/Acces ... rChargeKit
And to connect to your PC, you'll need this wireless gaming receiverhttp://forums.xbox.com/gfw/forum_faq/f/ ... spx#177655
make sure you get the genuine one
If you use a wireless controller, you can only connect to the PC using the wireless gaming receiver. You can't use the wireless controller and connecting it to a USB via the play and charge kit. So you CAN still use the controller while charging it if you had the wireless gaming receiver though. Hope that clears up your question.
They also had a quick charge kit, but using this you can't use the battery while charging.http://www.xbox.com/en-US/Xbox360/Acces ... kchargekit
For the PS3 controller, I guess you can say that, yes the receiver is a bluetooth receiver (in this case my bluetooth receiver on my mac). But I'm not sure if other bluetooth receiver will do the same, I'm not sure how the bluetooth works.