An email address is a complete solution which you can use to both send and receive emails.
A forwarder is an email address that forwards emails to another existing email address. You can't send emails with it.
A catch-all email address is just like a forwarder - it forwards all emails. The big difference is in the fact that a catch-all email address works for all email addresses that don't already exist. So, suppose you have only created email@example.com as the email address for your domain name, and someone sends an email to a non-existent email address, such as firstname.lastname@example.org. A catch-all email address will then receive that email and forward it.
At Site.eu, when you create an email address, you can very easily choose whether to create a forwarder or a full email address.