Like most things in life, people tend to fall somewhere in the middle between polar opposites.
Let me explain.
Let's say you are going to bench press and you decided that you want to use a weight that will allow you to get around 8 reps per set.
The HIT approach: You are planning to do one all out set with 275. So you do a brief warm up, something like 135x8, 185x3, 225x2. The warm up is very brief because your focus is the one all out set with 275.
The volume approach (the textbook volume approach). You are going to do 4 sets of 8 with the same weight. Now if your best set of 8 is 275lbs, you know you won't be able to use that weight for all 4 sets. So your workout might look something like this: 135x8, 185x5, 225x8,8,8,8.
The blurred line : You are going to pyramid up in the 6-9 rep range. So your workout might look like this: 135x9, 185x9, 225x6-9, 275x6-9 . This isn't HIT, because there is fatigue being accumulated during the work up sets. It's really not volume since you are not repeating any sets. And you are really working up instead of just warming up.
The third approach is generally what people gravitate toward to once they have been training for several years and have reached the intermediate stage ( squat 1.75xbw, bench 1.5xbw, deadlift 2xbw,standing overhead press 1xbw, weighted chin up/pull up bw+50%).
The one draw back of this approach is that it's difficult to see where the warm up sets end and work sets begin, this is more than just a minor detail, because the overall workout volume and training load is affected by what weights you are using for your work up sets.
