the third harness is for the vehicle speed sense and steering wheel controls and sub if you have them. that plug doesn't go to anything with an aftermarket headunit. that harness you got is correct. the black one plugs in to the yellow factory plug and the grey goes to the black factory plug. one of them is a different size, but just line up the clips in the center and you're good.
did you get the dash kit and antenna adapter as well?
2013 F150 4x4 SCrew XLT 5.0L
Midwest Crew #22
Official FocusFest Event Planner