Stijn,
If you do an Advanced Find as you describe, you are counting the number of Contacts who clicked any link. In your example, it sounds like there were 19 people who clicked a link. This is how our Click Report also works.
Our statistics graph on an Email Send shows the number of unique clicks by unique recipients. Some of the 19 people clicked more than 1 link in the email. If I click two different links in the email, that is 2 unique clicks.
There are different ideas about how this should be measured/counted, and our Click Report was built several years ago based on the current thinking at that time. The email statistics in the Email Send represent what we believe to be the numbers that most marketers are looking for these days. We have not changed the click report because some customers have grown accustomed to that method and want to continue to compare numbers from current email jobs to older ones.