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.
A → B + C
Basically the opposite of an addition, a single reactant will split into two separate products. However, please note that one product is usually a fairly small molecule as compared to the other. For example:
A–B + C–D → A–D + C–B
A specific group or atom on one reactant is swapped out with a different group or atom on a second reactant. They "swap partners" and its a substitution. In above example, the B and D groups swap positions.
A → B
Here a single reactant will change the way it is arranged and give a new product with all (or close to all) of its original atoms.
✶ The star is next to addition because it is reaction of interest in the making of plastics/polymers.