Do I need both the screen and the digitizer?

I was getting random ghost touches on my Surface Pro 2 screen, and I was told the screen needed replacement. I managed to get it open, but apparently the screen and the digitizer are sold separately. Do I need to replace both, and if not, which one? And most importantly, how do I get the two apart?? Bottom line: it might not be worth the effort to save a few $ by reusing one or the other, but I can’t help trying.