Pagefind uses an index that is created ahead of time and stored as numerous files on a static site. It then downloads just the part of the index needed to complete the search. This means that you can search vastly more data than could be loaded onto a browser.
I think Pagefind is focused on the whole experience of searching pages, like with default UI widgets, easy page indexing, and handling larger sites. fuse.js seems to be a fuzzy-filter function on JS data, not handling the site integration.