How Natural language processing and elasticsearch are related
Natural language processing (NLP) is a field of computer science, artificial intelligence, and computational linguistics.
ElasticSearch is a search engine based on Lucene.

ElasticSearch uses parts of NLP (e.g., tokenization and stemming). ElasticSearch also includes software engineering elements to ensure a search solution is performant.
Since NLP is entire discipline, there are many parts of NLP that are not related to ElasticSearch.