The sun room is an American name for a conservatory, which is also known as a patio room, solarium or greenhouse. (Note: Greenhouse has a completely different meaning in the UK, being a small glass build outbuilding which is used for growing plants.)
Why do the Americans use a different name for a conservatory than here in the UK? (Please contact us if you have the answer, we haven't yet managed to find out, despite a number of enquiries.)
Sun Rooms are not as popular in the US as the conservatory is in the UK, this is mainly due to the weather, it is much more variable in the US with only a few states (The New England coastal region etc) really hving the climate for sun rooms to be a valuable addition to a property.
In the UK the term sun room is most commonly used for the lean to garden room, which is a style of conservatory that usually has a roof which slopes away from the building, to which it is attached, and three flat sides. The side parallel to the building is most often the longest side of the lean to conservatory.