There are a few different ways to do this. 

You can do it with two separate forms as you have described. Build the first extensive form for the external users to fill out. You can then copy the form to make your internal form and add the additional internal only fields. Set up a user task with the internal form and you should be good to go. If you don't want to copy the original form (or you add additional fields later on), you can also add those fields to the internal form individually. When you go to the layout designer, instead of dragging a field on to the form, go to the Variables tab and drag on an existing variable. If that variable is filled by the external user, that data will pass into the internal form. 

Or you can do this with a single form using field rules. The key here is that the external user will have a blank username when filling out the form. What you can do is add a single line field (User) to the bottom of your form, make it read-only, and set it to a default value of Current User -> Username. Then using field rules, you can 

Hide User Always

Hide Internal Section when User is blank

That way, when the external users are filling out the form, user is blank and the internal fields are hidden. When the internal user gets the same form, that hidden field is filled out and the internal fields section shows.