There is no difference in between the normal and the play and charge kit controller. Both are the same. The only difference is, that you get a battery pack and a USB-cable with your controller.
If you want to play on the PC, you can buy any other USB-cable and forget about the battery pack. In order to use the controller on the PC you'll need to permanently connect the controller to your PC using the USB-cable.
If you want to play on the Xbox too with the same controller, the battery pack is worth it. The battery holds about 10-15 hours if I play normally. This means, I never emptied it on a single session. The special about the USB-cable from the play and charge kit is the LED at the controller end. It will display the charge status of your controller.