Admins create Products either in the Storefront Products, which are generic products available to all your clients, or in the Products Section in a particular Clients Settings area.
Adding a product for one client only means it will only be available to that one client.
Please NOTE that when creating a product you must name it, and then hit SAVE. Once you save that product, more options and settings will become available, via the tabs at the top of the ‘Edit Product’ page.