What does Remy mean?
From the French Remigius, linked to the Latin remex, “oarsman.”
What does Roy mean?
From Old French 'roy/roi', meaning 'king'. Note a second, separate origin: the Scottish Gaelic nickname 'ruadh' ('red', of hair/complexion) — so Roy can mean 'king' (French) or 'red' (Gaelic) depending on the bearer.