newbie questions on black water tank and campgrounds

so, at a full hookup site, I let the holding tank fill up, and then I just dump it? and then let it fill up again? im going memorial day weekend for 3 nights.. they want $9.00 more per night for a black water hookup.. probably better off just saving the cash and just dumping before I leave. there are bathrooms right next to the campsite that im in..clean ones. now, also, gray water, does that get dumped into black water too, or do campgrounds have gray water dumpstations also? thank you