I'm answering because your question has languished, and not because I really understand its subtleties.
> ... I don't quite understand how it works. ...
The inner workings are not really described. The interface is described at the doc page I link below. If you want to understand how it works, rather than how to work it, there are plenty of articles on full text search technology to be found with a web search (which normally uses such technology.)
> For FTS4, is it just to speed up the search?
That is the primary purpose of FTS(anything), as <u>[the FTS{3,4} docs](https://sqlite.org/fts3.html#fts4)</u> indicate. I suggest you study them.
> ... but the results should be the same whether FTS4 is used or not?
The search using FTS relies on indexing of whole words, after they are subject to a "stemming" process. (You can find that in the linked doc or via a web search.) So for searches on words will turn up the same finds. Searches on parts of words are likely to turn up different results depending on whether FTS is used or a more brute-force searching/sifting method is used.