The three following search methods are always available on all search pages whereas it doesn't always make sense:

1. Indexed search
2. Indexed search with advanced query syntax
3. Direct search (which might be renamed after MBS-12788)

Documentation search is neither indexed nor direct, it uses Google Programmable Search Engine (for now at least, see MBS-10290 for follow-up).

Direct search was the old default method. Nowadays it is only available as a fallback for when the indexed search is either unavailable or missing some (past or future) index updates. It doesn't make any sense to propose this method when no other method has been tried before.

The methods are documented but their names are not really telling much to the users, it is mostly developers' verbiage.