Not really. If I did a chest workout with 4 working sets to failure of 12-15 reps apiece, would you call that high volume? I wouldn’t.
I mean more sets, more reps at least close to failure. Usually achieved with pyramids / progressively more difficult warmup sets, intensifiers, clusters, and / or just a larger number of sets.
Actually my total failure or near failure sets for legs aren’t that high, but I do a lot more volume on the way up to the top weights. Higher rep ranges for legs and usually arms, but that’s not exactly the same. I do that because it’s more joint friendly and especially with legs, once you’re strong, low reps is playing with fire.
You often see huge bodybuilders hitting sets of 6-8 on pressing movements, but not so much on leg press, hack, etc. Just a lot of joint stress for not much payoff.