"Pharyngeal" refers to resonance, whereas edge refers to a component of healthy cord closure: two quite different- yet inter-related ideas. In order to avoid negative strain as you ascend through your 1st bridge, you must shift resonance from your chest to your head voice. The "head" resonator in the back part of your nasal cavity. The "pharyngeal" resonator is in the front part of your nasal cavity and adds loudness and fullness to the mixed voice.
In order to have full resonance, in any resonator, your must have adequate cord closure. "Edge" exercises are intended to help you find closure in the smallest of the vocal folds. Having "edge" in the voice allows you to achieve cord closure at low volumes.
By Jeff Mathena