Sinusitis. Most sinus infections start out as viral infections. It is often based on clinical diagnostics and length of duration that allows a physician to debate if the infection is bacterial. In order of most to least frequent = viral > bacterial > fungal.
Infectious sinusitis. Is usually 3 types viral, bacterial and fungal. Bacterial sinusitis is usually caused by strep pneumonia, haemophilus influenza or moraxella.
Sometimes. Sinusitus is an encompassing term that just states inflammation of the sinus, which can be due to allergy, infection or an autoimmune issue. It is possible if you have sinusitis due to a viral infection, which in turn causes "clogging" of your sinuses, which can get super infected with bacteria.