Ball lightning is, as the name suggests, balls of lightning produced in a thunderstorm. They usually occur after intense flashes of lightning, and are usually described as 'balls of fire' 1-100cm large, and not usually lasting more than a few seconds. These balls have very similar properties to earth lights, except ball lightning tends to explode rather violently. They may have exactly the same process going on behind them, except that the power involved in ball lightning is much greater. Earthquake lights were included in the synonyms for earth lights, but deserve their own explanation for reasons that shall become apparent.
Earthquake lights are lights that are observed during earthquakes near the faults involved.
Thus, you can see the relevance to earthquakes. An eye-witness account of earthquake lights. The Most Famous Cases. Hessdalen Valley, Norway. The Longdendale Lights.