An ecosystem and a watershed can be equivalent but need not be. Any one watershed may encompass multiple ecosystems, and a sufficiently large ecosystem will encompass multiple watersheds.
A watershed can be defined based on topography and water flow: "A watershed is an area of land within which all surface waters flow to a single point." An ecosystem may be harder to define or envision because it does not necessarily have a fixed physical basis.
Whether one defines an ecosystem or a watershed as a project area is immaterial in the technical sense. The Corps guidance on both ecosystems and watersheds includes factors of integration, maintenance of ecological processes, and the human component.