why self private method different private setter

self_private.rb

class Example
  def initialize(name)
    @name = name
  end

  def test_equal_private(ex)
    self.private_property == ex.private_property
  end

  def test_equal_protected(ex)
    self.protected_property == ex.protected_property
  end

  def private_setter(value)
    self.private_property = value
  end
  
  def private_getter_print
    puts private_property
  end

  def print_name
    puts @name
  end

  private
    def private_property
      @name
    end

    def private_property=(value)
      @name = value
    end
    
  protected
    def protected_property
      @name
    end

    def protected_property=(value)
      @name = value
    end
end

e1 = Example.new('e1')
e2 = Example.new('e2')

# puts e1.test_equal_private(e2) #(NoMethodError)
puts e1.test_equal_protected(e2) #false

e1.private_setter('wtf')
e1.print_name() 

e1.private_getter_print()