How are these structures different?

Question

Ruby on Rails

There are two pieces of code:

module Admin
  class CategoriesController < AdminController

and

class Admin::CategoriesController < ApplicationController

What is the difference? In both cases, everything seems to work as it should. And which one is correct?
PS I understand that there is no correct one and both are identical.
Sorry, I'm still learning.

Answer 1

There are differences. In the first case, the code inside the class will see the constants from the module (and the names of nested classes, respectively), but not in the second.
Example:

module A1
  TEST = 'zz'
end

module A1
  class B1
    def foo
      TEST
    end
  end
end

module A2
  TEST = 'zz'
end

class A2::B2
  def foo
    TEST
  end
end

A1::B1.new.foo #> "zz"
A2::B2.new.foo #> NameError: uninitialized constant A2::B2::TEST

Answer 2

first google link for "rails modules": rubyclub.blogspot.ru/2012/10/ruby_869.html