What's the difference between typical and atypical pneumonia?

Very little. "atypical" pneumomia is actually very common. "typical" pneumonia is caused by conventional bacteria, usually with a capsule. Most atypical pneumoia is caused by small organisms (mycoplasma, legionella) that infect the inside of the cell, as opposed to living outside the cell.
See below. Atypical pneumonia is pneumonia caused by mycoplasma, chlamydophilia and legionella species as opposed to usual bacterial pneumonia caused by other bacteria like streptococcus pneumoniae.