To create a Shared search you have to either Save the search in one of the Default Categories (except My Searches) or in a custom category that was set to Shared. All of the default categories are set as Shared categories. If you create a category as Private, only Private searches can be created in that category. In addition, once a Search is saved as either Shared or Private you cannot modify the type after it is saved. You would have to do a Save As and then you can change the name and set it to Shared or Private.