external means the link will go to the external network of you. if rel="me" then the link shows that it is your other site
when you are checking the link relation if it is external and shows nofollow the link is absolutely is of no use, it will not be considered as back link. see to that the link secured or developed is followable and also not redirected one.
only no follow makes a difference in google, the rel tag was intended to tell spiderbots and for later development to tell bots what the connection or relation is with the current site and with the site being linked to. They wanted it to be used like this: <a href="http://forums.digitalpoint.com" rel="seo forum">Digital Point</a> <a href="http://fakeurl.myspace.com/" rel="friend">Slincoln's Friend</a> Code (markup): The rel is not meant as anchor tags, but rather the relationship. In the first case we denote Digital Point is an seo forum to us, someone else may set their relationship to Digital Point as "domain marketplace" and that denotes that the relationship of digital point to that site is as marketplace for domains. In the second example, we denote that the myspace page is a page of our friends. Your friend may link to that page as rel="me" indicating it's their page, or their cousin may link to it as rel="cousin" denoting a familial connection between the linker and linkee. The point was that bots would be able to recognize and add meaning to what these links are rather then just as static links.