'Link' backlinks are all hyperlinks (ones you click on that take you to
the site) and are the most important backlinks you want to get for your
site.

'Contain the Term' links are plaintext url address links that you can't
click on but only show the doamin name or url address in plain text
format. Those are also important and good backlinks to have but no where
as important as regular 'Links' are as backlinks.

Sometimes google will show links that are hyper and clickable in the
contain the terms section. Why I'm not sure and it could just be a
google bug (there are lots of them) but eventually they do go to regular
'links' section.