As far as I can tell, Lucene is the library that powers the main search-related features of Elastic Search i.e. inverted indices, stemming, tokenization, etc.

Elastic Search, Amazon Open Search, Solr, etc. just wrapped Lucene up in a much easier to use HTTP / Rest API and then added bells and whistles like a coherent DSL, scripting, authentication and authorization, jobs, bulk API, etc. Then they built additional tools like Logstah and Kibana, which integrate using these APIs.