Difference between resource and resources methods

Actually you are right, resource should not create an index action, unless you ask for the index action explicitly, this way:

resource :orders, :only => [:index, :create, :show]

Helpers should differ too, but not that much as in your example, because the convention is to use a singular form with the resource method, and the plural with the resources

resources :orders
=> rake routes

     orders GET        /orders(.:format)            orders#index
            POST       /orders(.:format)            orders#create
  new_order GET        /orders/new(.:format)        orders#new
 edit_order GET        /orders/:id/edit(.:format)   orders#edit
      order GET        /orders/:id(.:format)        orders#show
            PUT        /orders/:id(.:format)        orders#update
            DELETE     /orders/:id(.:format)        orders#destroy

resource :order
=> rake routes
      order POST       /order(.:format)            orders#create
  new_order GET        /order/new(.:format)        orders#new
 edit_order GET        /order/:id/edit(.:format)   orders#edit
            GET        /order/:id(.:format)        orders#show
            PUT        /order/:id(.:format)        orders#update
            DELETE     /order/:id(.:format)        orders#destroy

And the logical difference is to declare you logically can't have the plural for resource in your app, for example Admin or whatever

At a high level, the intent of resource is to declare that only one of these resources will ever exist. For example:

resource :profile, :only => [:edit, :update]

As a user, I should only be able to update my own profile. I should never be able to edit other users' profiles, so there's no need for a URL scheme like /users/1/profile/edit. Instead, I use /profile/edit, and the controller knows to use the current user's ID rather than the ID passed in the URL (since there is none).

That's why you don't get an index action with resource: there's only one resource, so there's no sense in "listing" them.