There's a proper way and an improper way to carry guns in public. When you're carrying your gun in front of you with your hand on the grasp, you're carrying in an improper way. Properly would be gun n it's holster or slung across the back on a strap with the barrel facing down.
The first guy is carrying legally in the proper way. Slung snug across back, barrel facing down. The second is not. The second guy is more likely to be arrested as his hand is on the grip with the gun in front of his body. If he were at a shooting range it would be fine as he is holding his gun in preparation of using it but is keeping his finger off the trigger until he aims. Since he is NOT at a shooting range this can be seen as threatening and dangerous. Don't be a dumbass with guns like the second guy or any of the guys in the video provided. Be the first guy the safe guy, the guy who doesn't grasp his gun like a security blankie.