Actually Lucene is the library for search that Elastic uses under the hood. Lucene does not provide any HTTP API, which Elastic does. Before using Lucene, you have to build the interface around it.
In this way MeiliSearch is comparable to ES, especially for site search and app search working out of the box as standard with its http api.
MeiliSearch does not offer distribution yet, but it is something the team is working on :)