What is the difference between anticoagulants and fibrinolytics? list the ones discussed and designate their class.

Their difference is that anticoagulants (thrombolytics) act on the entire thrombus or clot. Example, Heparin - it is the a natural thrombolytic and is administered directly into the blood vessel.

While fibrinolytics break down the fibrin within the clot. 
Plasminogen is an example and is highly dangerous and can cause death. So never use this drug without consulting the doctor first.