A remarkable characteristic of earthquakes is their clustering in time and space, displaying their self-similarity. It remains to be tested if natural and induced earthquakes share the same behavior. We study natural and induced earthquakes comparatively in the same tectonic setting at the Coso Geothermal Field. Covering the preproduction and coproduction periods from 1981 to 2013, we analyze interevent times, spatial dimension, and frequency-size distributions for natural and induced earthquakes. Individually, these distributions are statistically indistinguishable. Determining the distribution of nearest neighbor distances in a combined space-time-magnitude metric, lets us identify clear differences between both kinds of seismicity. Compared to natural earthquakes, induced earthquakes feature a larger population of background seismicity and nearest neighbors at large magnitude rescaled times and small magnitude rescaled distances. Local stress perturbations induced by field operations appear to be strong enough to drive local faults through several seismic cycles and reactivate them after time periods on the order of a year.