What's the difference between DNA appliance and Homeoblock?

Greetings from Sweden :-) I suffer from Malocclusion class 2, an overbite and a deep bite, around 10 mm in between. My lower jaw is too far back in regard with my upper jaw. I do have TMJ and my airways aren’t that open as I can feel it. I would like to advance my lower jaw and also expand both lower and upper arch. I have some minor problems with chewing. I’m more interested in having a stronger jaw and correct bite rather than teeth. Do I need the DNA or Homeo and will I need for both jaws?