Coal is not a fossil. Coal is carbon, i.e. an element, and is not a fossil of anything. Fossils can reside in coal, but the coal itself is not the fossil and the fossil is not coal.
A fossil is any solid artifact that provides information of some previously living thing. Carbon does not come with historical information. Any given carbon atom might have been a part of millions previous life forms but it can't reveal any information about any of them.
Coal is an allotrope of pure carbon. It is what burns (only when oxygen is present) and produces CO2. Of course there are impurities in coal, with varying coal veins having varying levels and types of impurities. The impurities do not burn. Sometimes those impurities are fossils; they don't burn because they are impurities. Only the carbon burns. The purer the coal the better it burns.
There are four types of coal: Anthracite, Bituminous, Subbituminous, Lignite
Anthracite: lustrous, deep black, excellent quality, rather hard, very low on impurities.
Bituminous: shiny and "layered", very good quality, the most prominent in the US for generating electricity.
Subbituminous: dull black, good quality.
Lignite: brown, acceptable quality, with the least concentration of carbon (high amounts of impurities).