We expand Reames’ tabular summary of the two‐class picture of solar energetic particle (SEP) events to include characteristics of the particles that interact at the Sun to produce gamma‐ray emission. This addition underscores the contributions of gamma‐ray observations to our current understanding. The broad picture that is emerging is remarkable for its simplicity: while SEP events come in two basic types depending on the duration of the associated flare, the interacting particles in impulsive and gradual flares appear to be indistinguishable and resemble the SEPs observed in space following impulsive flares. The expanded classification system includes hybrid events, i.e., flares in which the gradual/impulsive distinction is blurred and for which the SEP events contain a mixture of flare‐accelerated and CME/shock‐accelerated particles. We argue that SEP events associated with long duration flares can be expected to have a temporally and spatially confined ‘‘core’’ of flare‐accelerated particles surrounded by a ‘‘halo’’ of CME/shock particles. Thus SEP composition should be checked in comparative studies of gamma‐ray emission and particles in space to ensure that the SEPs are flare‐accelerated. We discuss how recently‐discovered types of gamma‐ray flares (electron‐dominated events, spatially and temporally extended gamma‐ray events) may fit into the expanded classification scheme. We suggest that the acceleration process in the pion‐rich phase of large flares (e.g., 1982 June 3) is similar to that occurring earlier in the flare, the main differences being the greater height of the acceleration region and the presence of previously accelerated seed particles.