Extrinsic asthma is where things outside your body cause you to have asthma symptoms (shortness of breath, chest tightness, etc.).  The things outside your body would include pollen, molds, cigarette smoke, pollution, etc.  The treatment for it is bronchodilators and corticosteroids.

Pneumonia is where you get an infection in the alveoli of your lungs, and this results in inflammation inside the alveoli. Your lungs are normally sterile, so an infection in the lungs is a big deal.  The only treatment for it is time and antibiotics to kill the infecting bacteria.

Instrinsic asthma, by the way, is where something inside your body is triggering your asthma.  Examples would be acid reflux (GERD).