Yes, do NOT train to failure on each set. You should be able to have maybe 1 or 2 reps left after your first set. This allows you to do more work overall, as it doesn't tax your Central Nervous System nearly as much.
Yes, every once in a while, forced reps, or training to failure can be beneficial to change things up ONCE IN A WHILE.
Not training to failure, or leaving a couple of reps in your set has been proven to be far more effective for muscle gains and strength gains. That is why many articles here will say to choose your 6 rep max (the amount of weight you can just bearly get 6 good reps with) and do sets of 3 or 4 with that weight.
In the Anti Bodybuilding Hypertrophy program, Chad has days where the weight you use is your approx. 5 rep max, and do 10 sets of 3. If you used your 3 rep max, there would be no way you'd get all 10 sets in with 3 reps.
That way you would be getting 30 total reps with your 5 rep max weight. If you did all 5 reps on each set, you might get 2 sets of 5, 1 set of 4, 2 sets of 3, and 5 sets of 1 with that weight. That would be a total of 25 total reps.
Now that's probably not accurate, but it was just to show my point. I probably wouldn't be able to even get 1 rep after 6 sets to failure with my 5 rep max.
About your question "does this apply to
all types are training? (For example
training for strength? Hypertrophy? or
Definition?", nutrition and some cardio plays more important roles when trying to lose fat, or "train for definition".
It's a good idea to continue to train as if you're trying to gain muscle or strength, to keep or even possibly gain some muscle while losing fat.
Hope that helped.