Given that module Foo is defined elsewhere what is the difference between this snippet:

class Foo::Bar
  ...
end

and this:

module Foo
  class Bar
    ...
  end
end

Answer inside ;)

Given that module Foo is defined elsewhere what is the difference between the following 2 code snippets?

class Foo::Bar
  ...
end

and this

module Foo
  class Bar
    ...
  end
end

It is actually quite simple. The following code:

# foo.rb
module Foo
  BAR = 123
end

module Foo
  class A
    puts BAR
  end
end

class Foo::B
  puts BAR
end

will output:

123
foo.rb:13:in `<class:B>': uninitialized constant Foo::B::BAR (NameError)
  from foo.rb:12:in `<main>'

Simply put, while A has access to the insides of the module’s Foo namespace, class B is defined outside of this namespace, only the result of the definition is put as a constant inside Foo.

I most frequently stumble on this when I want to define some common constants in the parent module, just like in the example above. Given that and the fact that the 2nd form doesn’t actually require the module to be defined, the 2nd form is probably better and is a safer bet in most cases.