You could say they are the same molecule, but a molecule whose function is to change its state and properties very quickly when activated by thrombin.
Fibrinogen is a soluble protein - a complex of six protein chains.
Thrombin is an enzyme called a protease which very specifically cuts the ends off of two of those protein chains.
Once those bits are removed from Fibrinogen, the resulting molecule creates fibers very quickly to form clots.
You could also say that fibrin is a different molecule than fibrin because it really consists of many fibrinogen fragments.