I am aware of the fact that there are several different types of pneumonia.
However, I am wondering if any of these types of pneumonia are contagious from person to person. Is this possible?
Pneumonia means inflammation of lungs- especially alveoli. There can be many causes of it including infectious agents, autoimmune condition and chemical irritants. Pneumonitis is a more accurate word for lung inflammation, the causes of which includes the abovementioned agents; Pneumonia in common usage refers to the condition due to infectious agents such as bacteria, viruses and fungi.
In almost all the cases the infectious agents are airborne in the form of aerosols (spread by cough) and infect the respiratory tract directly. Some cases of fungal pneumonia (Pneumocystis, Penicillium) are observed more commonly in immunocompromised individuals, such as AIDS patients, and dissemination happens via spores.
As you can intuitively figure out the infectivity is different for different pathogens.