A cycloaddition reaction is actually a type of pericyclic reaction, but the term “pericyclic” includes other types of reactions. The textbook definition of pericyclic is a reaction whose transition state has a cyclic structure (i.e., the electrons are flowing in a closed loop). In addition to cycloaddition reactions (which exchange two π-bonds for two σ-bonds, or vice versa), pericyclic reactions include sigmatropic reactions, electrocyclic reactions, and cheletropic reactions (and a few others which we’ll ignore).