Not To Be Confused With
Modalism collapses the three persons into one; Arianism keeps them distinct but demotes the Son. The “water/ice/steam” and “one man as father/son/worker” analogies actually teach modalism.
Modalism saves the oneness of God by sacrificing the distinction of persons — so it cannot explain the Son praying to the Father or the Spirit sent by both. The Cappadocian grammar (one ousia, three hypostases) guards against it.