Most guys do not pay attention to minor aspects of lifting that can have major affect on the technique of lifting weights. There are more than one grips that can be used to hold a barbell and different grips have different benefits.
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The way most of the guys while doing chest workout hold the barbell is overhand grip in which back of your palm faces towards you. Lifters who use overhand grip most of the time wrap their thumb around the barbell and that is called full grip and closed grips. In closed grip you can squeeze the bar as hard as you could.
Underhand grip is one in which bar is held in a way our palms faces towards us and this type of grip is used while doing barbell curls.
If in overhand or underhand grip your thumb does not wrap completely around the bar than you are using false grip and it could be dangerous to hold the bar with false grip while doing chest workout because there are chances that your hands can slip.