I have a website that has 100+ articles with tags. What are some of the best search bar options available out there?
I see things like algolia (https://www.algolia.com/) but are there other alternatives? And how sophisticated are these search algorithms, just based on pure keyword matching?
Algolia is the state-of-the-art.
Try them out first, and if there's anything they don't have that you need, ask for that in particular.
BTW, I have seen websites adding the Google search box as well.
Do they do things like smart search concepts? (by mapping neighboring vector space with search terms)
For example, Let's say I search "jet" but my article only has the word "rocket". We as humans know that this may be a valid result to show but a keyword matching algorithm won't. Is algolia smart enough to figure this out or is it just a really reliable and fast key word matching algorithm.
+1 for Algolia. Used them at my employer and it doesn't get much better than them.
https://aws.amazon.com/cloudsearch