Is it the whole display or just the front glass?

No, yeah. Your "touchscreen" consists of two parts: 1.) Digitizer (a.k.a. literally the glass) and 2.) The LCD screen (the actual touchscreen that shows you your home screen, pictures, videos, and accepts your touch). These two components make your Note 3 screen, as one single entity (or part). The manufacturer (Samsung, in this case) are the ones to decide this, and actually, most if not all manufacturers are making ALL their screens as 1 part total as far as I'm concerned, from this point on. The reason be, because obviously they want to make it harder for repairmen or "rigmen" to separate the Digitizer (the glass) and the LCD (the "touchy screen" part), unless you have a specific equipment to separate them. Even with the special equipments, trust me, its still pretty hard.

That being said, sure, you may have to only replace the Digitizer (the glass), but you would have to go through the same separation process like I mentioned above. And that's if the Note 3 assembly is just like the previous Note's, and haven't included a "curveball" to throw you off. I haven't disassembled one yet, just waiting for someone to provide a guide first.

Have a local phone repairman take a look at it, ask him/her if just changing the Digitizer (be specific, say "the glass") would fix it, based on their expertise. If they say thats a possible option, you just pay the Digitizer (the glass), which is really cheap like $10-$30 bucks, and you just pay their labor.

Unless you wanna do it yourself, go right ahead bro, just saying.