From AMS Glossary
The K process is generally viewed as a recoil streamer or small return stroke that occurs when a propagating discharge within the cloud encounters a pocket of charge opposite to its own.
In this view, the J process represents a slowly propagating discharge that initiates the K process. This is the case for K changes in cloud discharges. It is reasonable to expect that cloud discharge K changes are similar to the in-cloud portion of ground discharges.