Silence gives you a 1 point (100%) muffle effect permanently. Muffle works whether you are in or out of sneak. With this perk it is very possible to run up behind people and have them not detect you.
Shadow Warrior takes you and your enemies out of combat by applying a very short invisibility buff. If they are unable to detect you (which is easy with high sneak and perks) then they will search for you and soon after go back to their usual routine.
Basically..
Player crouches -> Enemies can detect you within this one second~ invisibility period -> Combat continues
Player crouches -> Enemies cannot detect you wtihin this one second~ invisibility period -> Enemies search for player
Shadow Warrior can be used to get in combat sneak attack criticals and to quickly lose enemies without having to entirely flee the area.