To be clear, the Port Authority Bus Terminal is the main bus station in NYC where most Greyhounds (and most other traditional intercity buses) arrive/depart.
Penn Station is just a few blocks south of the Port Authority and is an underground train station (it's the main station for Amtrak as well as two of the three major commuter lines). A lot of the new-school intercity bus companies like Boltbus, Megabus and some of the independent Chinese and Jewish bus companies pick and up and discharge passengers on the streets surrounding Penn Station, but there isn't a formal bus depot or terminal of any sort there.