Two forms in register page Drupal
You can do it simple, add 2 form concurrent to the page you want ( if they are block  put two block in that page) and then with simple Jquery you can handle it with something like below code

(function($){
// change jquery selector with real ones
$('.user-register1,.user-profile-register').hide(); // or you can hide them with css
var selector= $('your radio option selecotr').value();
if(selector==1) {
     $('.user-register1).show();
     $('.user-profile-register').hide();
}
elseif(selector==2){
     $('.user-register1).hide();
     $('.user-profile-register').show();

}

})(jQuery);


This code IS the way how can you achieve it and if you copy/paste it it will not worked till you changes its selector and values with your forms