There are many routes that can be taken to any given destination. There is no “one right way”. That principle applies in many aspects of life, including your workout. The purpose of an exercise is to achieve a specific result in the body, whether it is trimming the waist, building a bicep, strengthening the core, increasing flexibility or improving endurance.
The primary rule is to stay within the parameters of safety while achieving the desired effect.
The reality is, there are countless possible variations on any given exercise. You must pick those that are most effective for YOU at achieving the desired physical goal while staying within those safer perameters.
Some say that when you bench press, you should bring the bar to the chest and touch WITHOUT bouncing. Others say not to touch the chest at all, because it puts undue stress on the shoulder joint by taking it past it’s natural weight bearing range of motion. Truth is, they both work! It depends on what works best for YOU. That’s what should determine which way that YOU do that exercise. Some say that when you do pull ups, always go to full extension (a dead hang) on each rep. Others say that for maximum effect, you should keep tension on the lats and never fully extend. Again, in reality, they both work!
Don’t let other people’s methodologies make you overlook what works for you. Do your research, or hire a qualified trainer to help you to learn your exercises and proper form for safety. Study and try the variations, and figure out which ways work best for you at achieving YOUR desired result while remaining within the range of safety.