There are hundeds of different specific reaction types in organic chemistry. There are subtle differences with each and many even named after the scientist who first discovered and utilized the reaction.
But if you survey a great number of the reactions you will find that there are a great number of similarities with many of the types of reactions. This allows us to narrow the scope down to a much more manageable set of reaction types. With a broad stroke we can think about having four fundamental organic reaction types.
A + B → C
Two reactants come together and join to make a new single combined product. Example below shows a common version of this where a small molecule ADDS across a double bond.