There are similar concepts, but they aren't the same thing. Smashmouth can be run out of bone formations, and typically features the fullback as a ballcarrier more than Powercoast would. A lot of option teams would be considered smashmouth.
The main difference comes from the passing game though. Power coast is just a west coast offense, with power running concepts. A power coast passing game still features a majority of snag and stick. The qb is typically only taking 3 and 5 step drops. Slants and passes to backs in the flat are a staple.
Smashmouth is "3 yards and a cloud of dust". The passing game is built off of playaction, and then taking shots downfield. The goal is to get vertical, and take the top off of the defense, when the safties come up, in your typical smashmouth O. You'll have QB's taking 7 step drops, and the ball travels a much greater distance, in the air, on average.
Example:
Jim Harbaugh = Power Coast
Rex Ryan = Smashmouth (Mike Mularkey, if you want an OC/HC example)
A Power coast is just an offshoot of the West Coast.