I use facetious and sarcastic in a similar way.
To say something you hold clearly isn’t true, maybe even the opposite, often exaggerated, in a manner that you intend it to be clear that you mean the opposite or something different.
Like if you see someone having trouble lifting a light load and you say: “You must be Mr. Universe.” That to me would be sarcastic.
Facetious to me would be something similar but without implied negative tones perhaps.
Two words I guess I use loosely perhaps incorrectly, but most people would probably understand my meaning quite well