view one = show, view many = index, whether its the admin viewing products, or a user viewing products, there's just one HTTP verb and url pattern in use... /products/ as a GET request.
If it were /products/ as a POST request, it better be accompanied by sufficient parameters to define the new product resource, since that's a RESTful create request pattern.
The basis of REST is the four HTTP 'verbs' GET, PUT, POST, DELETE.
Rails scaffolding builds REST out with 'standard' methods of:
index, show, new, edit, create, update, destroy
which pair a url pattern with one of the four HTTP request types
index: /plural_resource_name/ + GET - return a collection of the desired resource
create: /plural_resource_name/ + POST - create a new instance of the resource
new: /plural_resource_name/new + GET - return a new instance of the resource
show: /plural_resource_name/id + GET - return a single instance of the resource
update: /plural_resource_name/id + PUT - update a single instance of the resource
destroy: /plural_resource_name/id + DELETE - destroy a single instance of the resource