The mouth of a river or stream is a nebulous concept that is not all that closely defined. I typically take it where the shoreline of the lake, sea, river or other waterbody intersects the river or stream.

Usually extending out into the waterbody is the delta of the river, and it may influence the shoreline.

In fishing, I consider I am fishing the mouth if I am fishing near the mouth of the river, maybe up stream a bit, or on the delta, or maybe off the delta a bit.

And most tidewater rivers fill with saltwater at high tide. The Green does to Tukwila on big tides, the Stilly gets saltwater up it well past Marine View Drive.