Phaser power was the source from which phaser energy was derived, inasmuch as it could be delivered at variable levels.
Later, in the redesigned Constitution-class refit, phaser power was increased" by channeling it through the main engines," so when if the ship experienced an antimatter imbalance, its phasers were automatically cut off. (Star Trek: The Motion Picture)
Phaser power aboard the USS Defiant was "almost doubled" by "running the plasma conduit through the primary phaser coupling". The process, which normally would affect a starship's warp drive efficiency, actually increased the Defiant's by thirty percent. (DS9: "Defiant")