I think we are talking about a few different things.
A screenroom is more of a deck with screens and a roof.
They have wood planks for flooring with gaps to let water out. Maybe they will have a screen under the planks to keep the bugs out. They might not have any finished walls or cielings or some sort of sidding / paneling on the inside. Sometimes the wall is about 2" thick plus the sidding. Many times the structural members are exposed.
Some enclosed decks are the same but have more windows. I seen a mix of windows and screens. Sometimes they are not too different then a gazebo. The doors outside are a screen door. The door into the house is a exterior door. The room sits on posts set on cement piers. IMO these are not living space.

A finished sunroom has finished flooring, insulation, drywall, and maybe HVAC. They have at least a 2x4 wall and many times the cieling joists are taller to acomidate the required insulation. Sometimes they are wide open to the rest of the house. The doors outside are exterior or patio doors. The ones I seen always had full foundations on a slab, crawel, or basement. IMO this is a living space.