Redmine users relations
First of all, contact is not the same as a Redmine user. Contacts are more like anonymous users. If a contact sends an e-mail, the author of such ticket will be anonymous, because there is no such user in Redmine.
However, if there is a user in Redmine with the same e-mail address as the existing contact, these two will be linked to each other. In such a case, you will notice a link to the user's profile on the right sidebar called User with the link.
You can find more about contacts in this article.