There are many sources of roof staining and they vary in significance, from cosmetic to harmful to the roof.
As stated in Best Practices Guide to Residential Construction:
Black streaks on shingles caused by algae or fungal growth used to be limited to warm, humid climates, but now this can be seen on houses as far north as Canada. Some experts attribute the spread to the increased use of crushed limestone as a filler material in asphalt shingles.
Limestone is economical and makes a durable shingle, but the calcium carbonate in the limestone supports algae growth. In algae-resistant (AR) shingles, zinc or copper granules are mixed in with the colored stone topping. When the shingles get wet, the zinc or copper is released, inhibiting algae growth.
Warranties for algae resistance are usually for less than 10 years since the protection ends when the mineral washes away. Some shingles have longer lasting protection than others due to a higher percentage of AR granules.
The chemistry of roof shingles, their granule coverings, and substrates is quite different from other organic substances that are home to many molds. Further, many newer shingle products include chemicals to retard black algae growth that may also retard mold growth. Specific mold genera/species like to grow on particular surfaces - it's their food, and while some molds are more choosy than others (for example mildews grow only on living plants), you'll need to look carefully at a roof and the conditions around it (such as trees, and areas of sun or shade) and perhaps even sample the black debris to determine if it is mold and if so what is its species.
The roof cleaning methods to remove black algae will probably work well for black mold growth on a roof as well.