Chemical reactions are of many types. The main reason why different substances react with each other is that the product is a more stable compound than the compounds that form the reactants. Stability implies a decrease in potential energy.
When substances containing carbon and hydrogen react with oxygen to form carbon dioxide and water, it is a combustion reaction.
For example CH4 + 2O2 --> CO2 + 2H2O is a combustion reaction.
Synthesis reactions refer to reactions of the form A + B --> AB where two simple compounds A and B react with each to form a more complex compound AB.
The reaction of calcium with oxygen, which is expressed by the equation 2Ca + O2 --> 2CaO is a synthesis reaction.