They are the same when the air is saturated and the relative humidity is 100 percent.
Vapor pressure is the pressure produced when vapor particels above a liquid in a sealed container, collide with the container walls.
Temperature
No. It depends on the temperature. The only time you will really consider Pext is when you want to determine whether the substance will boil, which is when Pext = Pvap.
Vapor pressure at BP only will be equal to Atmospheric pressure