https://www.quora.com/How-does-Elasticsearch-relate-and-or-c...
tldr; Algolia's focus is on consumer-grade & user-facing search (searchbar like you would have on Amazon, IMDB, Twitch, Medium.com, quora, ...) while ES's sweet spot is on indexing billions of documents (or lines of logs) and provide rich dashboarding & aggregation capabilities (like a monitoring dashboard with their ELK stack). Recently, ES released a beta of "App Search" which seems to target more and more the user-facing search bars.
Here are also a few resources to help get you an idea:
* from Doug Turnbull, author of "Relevant Search" & ES expert: https://opensourceconnections.com/blog/2016/06/01/thoughts-o...
* from an Algolia & ES user: https://medium.com/@matayoshi.mariano/elasticsearch-vs-algol...
* from the Algolia FAQ: https://www.algolia.com/doc/faq/why/what-makes-algolia-diffe...
* from the Algolia blog: https://blog.algolia.com/?s=comparing+algolia+elasticsearch