The connections are different. Apple uses a smaller "ADC" connector which is pin-less and also carries audio, AV and USB, making it easy to build these features into the display.
I think there might be third-party adapters out there that will allow you to connect an Apple monitor to a VGA output, but I doubt you will get it to work correctly as there will be no drivers available. The studio display uses a resolution not common on PCs, I think.
The long and short of it is that, yes it is possible, but it isn't likely to be easy and you will undoubtedly meet all sorts of problems.