In some contexts they are synonymous - like formal/ceremonial/judicial/clerical costumes. A bathrobe can be called a robe but not a gown. A ballgown (posh frock) can be called a gown but not a robe.
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In some contexts they are synonymous -
like formal/ceremonial/judicial/clerical costumes.
A bathrobe can be called a robe but not a gown.
A ballgown (posh frock) can be called a gown but not a robe.
Also, in US English (Rover_KE is British) "gown" can only be used for women's clothing. "Robe" would tend to be used more for men's clothing, and usually for formal or ceremonial clothing only. Note: there's a famous American movie from the 1950s called "The Robe," which refers to a man's ceremonial clothing.