Water in the Western working traditions has the most consistent set of attributions of the four, and the consistency is worth pointing out because it is unusual.
In astrology water is a triplicity: Cancer, Scorpio and Pisces. In the tarot it is the suit of Cups, and unlike the wand and sword pairing this assignment is not disputed by any significant school, since a cup holds liquid and there is nothing to argue about. In the Golden Dawn system water is placed in the west, given the cup as its working implement and the archangel Gabriel as its regent.
The cup carries more weight than the other three implements because it arrives already loaded. It is the vessel of the Grail literature, the chalice of the Eucharist, the cauldron of Irish and Welsh material, and any ritual use of a cup in a European context is working inside that inheritance whether or not the practitioner intends to. That is a genuine difference from the wand, the dagger and the pentacle, which the ceremonial revival largely had to furnish with meanings.
Aristotle gives water cold and wet, heavier than air and lighter than earth, the element of flow and of dissolution. The later tradition adds the emotions, memory, dream and the unconscious, a cluster that is modern in its vocabulary and older in its substance, since the classical writers already associate water with the phlegmatic humour and with what cannot be gripped. Where a source presents the psychological reading as ancient, the attribution is real and the framing is not.
Sources The Golden Dawn: The Original Account of the Teachings, Rites, and Ceremonies of the Hermetic Order of the Golden Dawn, 6th editionIsrael Regardie with TetrabiblosClaudius Ptolemy