Comparison

The fundamentals of marksmanship are universal. Some different organizations put a different spin on them, but they are all inherently the same. 

Appleseed:

1. Sight Alignment

2. Sight Picture

3. Respiratory pause

4. Focus eye / mind

5. Squeeze the trigger

6. Follow through

Army: "BRASS"

Breathe

Relax

Aim

Sight 

Squeeze

NRA

1. Aiming

2. Breath Control

3. Hold Control

4. Trigger Control

5. Follow through

When you take this Army Designated Marksmanship Instructor's statement into consideration, you realize that while breath control or respiratory pause is important, it might be the least important of the fundamentals. Paraphrased, he essentially said between the 1:00 mark and the 2:00 mark: Someone who tells you to fix your breathing to tighten up groups has demonstrated they have a thimble full of knowledge of marksmanship. And he is correct. 

When it comes to pistol shooting for self defense applications, there are three main fundamentals that the shooter needs to concentrate on to make surgically precise hits:

• Firm Grip 
• Front sight focus
• Gentle squeeze of the trigger. 

At Fighting Pistol with Tactical Response, the instructors were often coaching participants to firm up their grip. One of them made it into a funny statement "choke it like a hooker!" They also coached trigger squeeze and front sight focus - but their emphasis was on the firm grip. 

At PistolCraft with Reid Henrichs (who was once an instructor at Tactical Response), the emphasis was on front sight focus and smooth trigger manipulation. He also encouraged participants to have a firm grip, but the emphasis was on trigger manipulation. 

When I teach, the emphasis is on the balance of trigger manipulation and grip. With a newer shooter, too firm of a grip will cause a parasympathetic squeeze in the trigger finger - resulting in shots low and left for a right-handed shooter; low and right misses for a left-handed shooter. There is an art to proper grip, as there is to proper trigger manipulation. I teach both. Good to know I'm in good company.