Ron nailed it.
Both repel, but Permethrin is for clothes but DEET is for skin (I also hit collars and cuffs if using a spray).
Pretreat outdoor clothing with Permethrin during summer months when the bugs are out (or more depending on where you live). Use DEET for your skin when you arrive on location. 30% DEET is ideal for most areas and 100% DEET for adults only in particularly nasty areas. I always start with 30%. If it is border line head net & gloves bad, the 100% juice comes out.