In the search for the shop you see always all items. I know you can filter but still if you search you will find items that are not in the shop but only in your product list (step1).

If you have season products you would like to remove some temperarely but not delete them you will need them a few months later again. If you remove these from your shop and set another collection in your shop the shop will not show them anymore, but the search will find them and you might get orders through the search. 

The only way around is to remove them totaly from the product list, but then you have to add them later on and recreate all these items. or export and import and make several imports and exports, anyway it's a hassle.

It would be very nice if you can set a hide button like on the pages, hide the category or the item in the product list with a hide and unhide button.

Then they should not apear in the shop and not in the search anymore. and you can set these on a few months later and other items off again, so you can easily handle your items according to season or holiday or whatever reason to use and don't use in the shop.

By the way the special pages names are the same for the shop, please rename 1 to search shop at least in Dutch, please check all languages and correct.