If the LCD is still working it's the digitizer. If the LCD is split into different colors (looks like it's cracked) then it's the LCD also. Rarely dies the LCD crack without the digitizer cracking too.
I just replaced a digitizer on my phone and it's a huge hassle. Don't attempt it if you haven't done it before or aren't comfortable almost cracking your LCD (if not already broken)
When you watch the videos, they make heating up and removing the LCD/digitizer easy and quick but it's not, it took me about 2-3 hours and I've done this on other non-glue phones.
You DO need to unglue the LCD even if replacing just digitizer (since the ribbon cable is behind the LCD and glued to it), if replacing both it shouldn't be hard since you don't have to be careful with the LCD