What a Medium Does That Water Cannot
Thinning acrylic with water and thinning it with a medium look similar in the pot and behave differently on the surface.
Water dilutes the binder
Acrylic paint is pigment held in an acrylic binder. Adding a lot of water thins the binder as well as the paint, and past a point the film that dries is weaker and can lift or chalk.
A medium keeps the binder intact
Mediums add more binder rather than less, so you can thin, extend or change the finish without weakening the paint film.
Matte, gloss and satin
The same medium family usually comes in different sheens, and the sheen carries through to the dried surface. Mixing sheens across a piece is a decision worth making deliberately.
Test first
Mediums change drying time and colour depth slightly. A test on scrap tells you more than a description ever will.