The two words get used as if they mean the same thing. They do not, and the difference shows up on the day you need it most.
Weatherproof means it holds up
A weatherproof bag will get you through a commute in steady rain. The face fabric sheds water, the coating resists it, and the contents stay dry because water never sits anywhere long enough to find a way through.
Waterproof means it seals
Waterproof is a higher standard: taped or welded seams, a closure that folds shut against itself, and no untreated stitch line anywhere water can pool. It is heavier, it is stiffer, and most people do not need it.
The failure point is almost never the fabric
Bags leak at zips and seams. A coated shell with an exposed zip will let water in along the teeth long before the panel gives up. This is why a storm flap and a reversed coil zip matter more than another layer of coating.
Match the standard to the day
If your worst case is thirty minutes of rain twice a week, weatherproof is the right call and the lighter bag is the better bag. If you are on the water or out for days, buy the seal.