Difference between resource and resources methods

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.

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#destroyresource :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