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IIRC, there should be three options: Hide, Show, and Show Icon. You could either show a search box (show) or a smaller button (show icon).
It's changed in later versions, because they've finally split the search option from Cortana. So now there's a "Show Cortana button" which is a single choice, and a "Search" menu with the "hide", "show icon", and "show search box" options.
But you don't expect consistency* from a Microsoft UI, do you?
* Apart from "the consistency of warm diarrhoea".
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
One gripe is that Microsoft started leaving "..." off of menu items that initiate a dialog.
They used to be fanatics about CUA compliance and "explorability" of the UI.
The Ribbon was the first step in removing explorability of the UI. Now there is a GIANT list of every possible command with no logical grouping that you can "add to custom". The GIANT list only supports single letter matching if you try to type! Hundreds of options start with "S".
Every thing is "Search" driven. You better know what you want and start typing it in to find it for any Windows 10 feature or program.
It was the Americans who declared their independence from the Britain, not the other way round. If Britain's leaving the EU is called Brexit, then America's declaration of independence should be called Amexit, or some such.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
-- 6079 Smith W.