Indeed. Only a small fraction of the collision events are kept, otherwise the amount of data would be overwhelming.
In particle physics, a trigger is a system that uses simple criteria to rapidly decide which events in a particle detector to keep when only a small fraction of the total can be recorded. Trigger systems are necessary due to real-world limitations in data storage capacity and rates. Since experiments are typically searching for "interesting" events (such as decays of rare particles) that occur at a relatively low rate, trigger systems are used to identify the events that should be recorded for later analysis. Current accelerators have event rates greater than 1 MHz and trigger rates that can be below 10 Hz.