I guess you COULD have both. One's inflammation in the colon from an infection in the diverticula (diverticulitis) and the other is inflammation in the colon from an immune disorder
An infection in the diverticula could easily spread out of that area and look like UC. Or UC could flare up in an area where there are diverticula and look like diverticulitis.
I guess the questions are:
a) Do you have diverticula in the first place?
b) Do you get better with antibiotics (they will treat an infection, but do nothing for moderate UC)