Yes, they are redundant.
Although the description for Sneak Lvl 4 does not say how running previously affected stealth, and therefore what exactly it changes, it probably works the same way as the Silent Running perk from previous Fallout games. Nukapedia agrees with this assessment. Looking at the Silent Running page, we read that
Fallout 4: The effects of this perk are found in the rank 4 of the Sneak perk.
That page also describes the effects of the Silent Running perk, saying that
Silent Running completely negates ALL movement penalties, regardless of movement speed. The detection level for the player character is the same, when standing still or moving around, no matter if moving slowly or running around.
Therefore, there are no "penalties due to movement" for Muffled to reduce.
Update from Experience
I've now experienced days of playtime with characters who have Sneak Lvl 4.
The only time my movement while crouched seems to cause enemies to detect me is when it changes how much of me they can see (like going around a corner, moving through bushes, or stepping into the light), when they can see me and I move closer to them, or when I knock something over and it makes noise.