One option would have been to use multiple views in your form and not have to
have two seperate ones. That would probably be best practice if the dat is
the same.  There are methods to identify the user so that you can secure each
view and route the user to the correct view.

To start a new form you have to have both forms published seperately. Just
create doc libraries which are not advertised.  You can add hyperlinks to the
templates on your main site insteaed of using the new form button.

Then each form can submit to the same doc library if that is what you want,
and maybe you have a view which keep the wrong people from seeing the other
type of forms. Seems like kind of a mess for them sharing it unless this is
some backend admin that can see both I guess.
There maybe some workflow that could work better.

Those are my thoughts. let me know if that helps.