Elasticsearch is a distributed search engine whose primary model is inverted-index text search, with vector search added alongside it. It solves the practical problem that most search is still keyword search, and a system that only does embeddings loses the exact-match behaviour users expect for names and codes. It exists because hybrid retrieval usually beats either approach alone, and running both in one engine avoids synchronising two.
OpenSearch is the Apache-licensed fork of Elasticsearch, offering the same combination of text and vector search. It solves the licensing problem that made some organisations unable to use the original. It exists because the governance of a search engine matters to the people who have to run it for a decade, and the fork diverged enough to be its own project rather than a copy.