Should SP sites published through TMG still be listed under local intranet settings or Trusted Sites? What is the difference?

Hello,

We are running SP 2010 Enterprise and Windows 7 Enterprise.  Our users are constantly being prompted for their credentials when opening and saving documents.

All of the posts I have found say to list the site in the Intranet Security zone settings.  My question is, is it still considered an intranet when a user is accessing the site from outside the network with the site published through TMG?

What would be the difference between havign the site listed here or under Trusted Sites?

Thank you!