PCP stands for Pneumocystis carinii pneumonia. Technically, Pneumocystis carinii is a fungus, but until recently it was always thought to be a parasite. Because it acts more like a parasite and responds to some antiparasitic drugs but not to antifungal drugs, for all practical purposes, it's a parasite.
Bacterial pneumonias can occur at any stage of disease.
PCP is more gradual in onset. It typically comes on over weeks, while bacterial pneumonia comes on over days. With other types of pneumonia, cough tends to be a bigger problem than shortness of breath. The cough of PCP is usually a dry cough, whereas people with bacterial pneumonia cough up lovely gobs of yellow or green or brown sputum. Bacterial pneumonias tend to respond faster to treatment.