Hi Tatopitta and welcome to our forum!
This is a great question. You can send your form to extranet users in one of two ways:
1. Restricted - set Tools->Form Options->Security to restricted and use File->Send Form as Attachment. This is limited in that your form can't do much due to restricted security.
2. URN-based - you can run Regform to create an MSI that you send to your users in e-mail. They install the form and then you have an e-mail data adapter in the form that sends e-mail.
In either case, you'll want to install the same version of the form as your users. Scenario 2 allows more scenarios but it doesn't support linkage with an internal SharePoint site. That's because the template.xml that is sent in e-mail will not have the URL for the solution, just the URN. Forms deployed on SharePoint require a URL.
You will have to create some logic in your URN form that loads the form and then launches the SharePoint version with it. In other words, you will have 2 forms. The extranet one with special launch code if it detects the internal SharePoint site and a form for the SharePoint site that includes a URL.
There are a bunch of other design patterns - you could create a winform for your extranet users that generates an InfoPath form with the URL for your internal site. We have done that before. This also doesn't require InfoPath for the extranet users, but it requires a lot of coding to create the Winform.
You could also use BizTalk or even the Import form functionality to import forms from e-mail into a URL-based SharePoint solution that acts as a dashboard loading and saving the forms from e-mail.
Hope this helps a little,
Patrick Halstead [InfoPath MVP]
InfoPathDev
Patrick Halstead
Project Manager at Qdabra