In my mind (and I could be wrong as everyone has their own opinion/desires/etc.) . . . a "sun" room would have large windows all around (as is possible depending on walls etc.) and room has lots of plants/flowers as to appear like a transition to bring the outside in and be able to soak up the sun.
Google result: "The term sunroom can mean slightly different things to different people. By definition, a sunroom is an enclosed room or porch specifically created to allow as much sunlight in as possible. Sunrooms have lots of glass or synthetic window materials — many include floor-to-ceiling windows and glass roofs. When people refer to a sunroom, many times they use the terms conservatory, greenhouse, sundeck, sun lounge, sun porch and solarium as synonyms although builders define these terms more specifically."