Her revival happened after the Mantle's Approach was destroyed, and the core of the ship made a slipspace jump to Genesis. Her rampant spikes, nothing more than shreds of code at that point, with unlimited space were able to repair and rejoin together effectively bringing Cortana back from the dead. So the Cortana we're seeing is the normal one; albeit with a different perspective due to her newfound ability to store memory and process large volumes of data as well as access galactic Forerunner systems remotely.