Puzzling question on backlinks I'm sure is really simple!!!

[skinz]

When I type in http://www.mydomain.com into Google, what's the difference between:

Find web pages that link to "www.mydomain.com"
And
Find web pages that contain the term "www.mydomain.com"

My guess is that the 1st relates to the number of backlinks, but why not the second? Also if I register my site with some SEO friendly directories will Google pick them up as examples of the 1st or 2nd of the 2 terms above? How does Google determine if the link from a site falls into term 1 or term 2?

Thanks