I think that by "screen room," an enclosed, screened-in porch (or rear deck) is what is meant. Such a place would have the outer siding of the house as one of the walls; the others would probably be of minimal construction.
I also recently installed a heater on an open terrace. Somehow the whole idea of 'standing outside' while seeking shelter from the elements fails to make any sense to me!
In the case of the heater I installed, the instructions were quite explicit as to clearances expected in different mounting positions.
#64934 - 04/22/0610:46 PMRe: Electric BB Heat on Vinyl siding
It's more of a "3-season porch" ....spring/summer/fall. You can opt for screens or glass depening on the weather.
Here's an inside look:
Notice the "exterior fixture" in the 1 O'clock position? Classic tip off of a "spontaneous construction" event...if they had planned this out better (or even at all) they would have ditched that POS fixture....also, see any outlets around there...any lamps/overhead fixtures?
People will simply "enclose" a typically rear porch and call it a "3-season" or "screened".