Taking into account you just started studying chemistry, and to expand Maurice' answer, I would reply your question of
"What counts as a fuel?"
that this depends on the reaction conditions set (e.g., temperature, concentration of the reagents present, pressure).* Then, any compound may be considered as a fuel provided it
- may be at all oxidized. This often is expressed in the release of energy which may be the emission of heat; yet emission of light, or the potential to perform mechanical work may be other forms. As burning logs of wood, more than one form (e.g., heat and light) may occur simultaneously. Chemists account for this release of energy (account similar like balancing a bank account) in terms of enthalpy, for example Gibbs free enthalphy. The more energy released, the better for compound x to be considered a fuel.
the oxidation proceeds rapidly. This is one of the reasons why hydrocarbons are used as fuel in combustion engines, because at set temperature and pressure in the cylinder, it is in a fraction of second that these react and release a lot of energy.
A counter example would be the oxidation of a nail of iron at ambient conditions. This reaction equally releases energy, but this is way too slow to be useful in an industrial process (by today's standards). Thus, it is not considered as a fuel.
*) For reactions with gases, there is some conceptual overlap of "concentration of the reagents" and "pressure". You may return to this detail later in your study.