It says walking and running will not affect detection, I would assume this means when you are not in sneak mode but then why sneak at all? Or is it moving very quickly in sneak mode? I would just like to know before picking it.

The perk only applies when you are in Sneak Mode.

Normally, if you run rather than walk while sneaking, then you are more easily detected. This perk removes the penalty for running while sneaking.

Better to just use the muffle spell. You can remain undetected when standing, but must move slowly. I'm not sure if the stealth perks play any factor.