Those definitions are not set in stone, and they mean different things to different people and to different volcanoes. One of the simpler ways to answer is that an active volcano is one that has erupted since the last ice age (i.e., in the past ~10,000 years). That is the definition of active used by the Global Volcanism Program in their catalogs. A dormant volcano would then be one that hasn’t erupted in the past 10,000 years, but which is expected to erupt again. An extinct volcano would be one that nobody expects to ever erupt again. These are human definitions of natural things – there have been a number of eruptions from “extinct” volcanoes!