what's difference between @ and @@ in a module?

Question

Assuming a module is included, not extended, what's difference between module instance variable and class variable?

I do not see any difference between two.

module M
  @foo = 1
  def self.foo
    @foo
  end
end
p M.foo

module M
  @@foo = 1
  def self.foo
    @@foo
  end
end
p M.foo

I have been using @ as @@ within a module, and I recently saw other codes are using @@ within a module. Then I thought I might have been using it incorrectly.

Since we cannot instantiate a module, there must be no difference between @ and @@ for a module. Am I wrong?

----------------------- added the following --------------------

To answer some of questions on comments and posts, I also tested the following.

module M
  @foo = 1
  def self.bar
    :bar
  end

  def baz
    :baz
  end
end

class C
  include M
end

p [:M_instance_variabies, M.instance_variables] # [@foo]
p [:M_bar, M.bar] # :bar

c = C.new
p c.instance_variables
p [:c_instance_variabies, c.instance_variables] # []
p [:c_baz, c.baz] :baz
p [:c_bar, c.bar] # undefined method

When you include a module within a class, module class variables and class methods are not defined in a class.

Answer 1

Class variables can be shared between modules and classes where these modules are included.

module A
  @@a = 5
end

class B
  include A
  puts @@a # => 5
end

Meanwhile, instance variables belong to self. When you include module A into class B, self object of A is not the same as self object of B, therefore you will not be able to share instance variables between them.

module A
  @a = 5
end

class B
  include A
  puts @a # => nil
end

Answer 2

@@ refers to class variable and @ refers to instance variable. While using this with module makes big difference. When you include a module you add class methods to your class while extending add instance methods to your class

Following is a nice article on this

http://railstips.org/blog/archives/2006/11/18/class-and-instance-variables-in-ruby/