One is an infection. Diverticulosis means that there are diverticuli present in the colon. Diverticuli are little outpockets of the lining of the colon (called colonic mucosa). By themselves they are usually not problematic, but these pockets can get infected. That is what diverticulitis is - infection of diverticuli. Symptoms include abdominal pain, tenderness, fever, and constipation.
Inflammation or not. Diverticulosis: the condition of having small outpouchings on the colon (large intestine). Very common, not related to polyps or cancer. Related to not eating enough fiber. Treated with high fiber diet and water. Diverticulitis: the pouches get inflamed or infected- happens to only 15-20% of folks with diverticulosis. Treated with antibiotics; abscesses get drained; surgery for complications.