create two different registration form with same fields without using profile2
Well you can make small form with 2 submit buttons (Register as A, Register as B) and post that data on register form, in this way you can hide it from url

OR

The other way which is more complicated, using ajax, when link is clicked and based on the clicked link you create the $form_state and set the flag then you call the register from using drupal_get_form and you pass the argument 

OR

Just create boolean field in user, and put the option (Register as A, Register as B) and make it required to be listed in register from