Q:

Using class << self, when to use classes or modules?

Is there a difference in usage between
class Helper
  class << self
    # ...
  end
end

and
module Helper
  class << self
    # ...
  end
end

When would you use one over the other?

A:

The class<<self seems to be a red herring, as the only difference here is a class versus a module. Perhaps you're asking "I want to create an object that I do not intend to instantiate, but which exists only as a namespace for some methods (and possibly as a singleton with its own, global, state)."
If this is the case, both will function equally well. If there is any chance that you might want to create a derivative (another object inheriting the same methods) then you should use a class as it slightly is easier to write:
class Variation < Helper

instead of
module Helper
  module OwnMethods
    # Put methods here instead of class << self
  end
  extend OwnMethods
end

module Variation
  extend Helper::OwnMethods

However, for just namespacing I would generally use a module over a class, as a class implies that instantiation will occur.

