this explanation is overly simplistic:
There's primary and secondary hemostasis:
Primary hemostasis is the formation of the platelet plug. This is when vascular endothelial injury is encountered and platelets go through that entire cascade, starting with vasoconstriction and vWF binding. The end result is fibrinogen binding platelets together (aggregation). This platelet plug is weak and easily dislodged. Issues here (eg. vWF disease, BS Syndrome, aspirin use, etc) usually present as small, mucosal bleeding and petechiae with an increased bleeding time.
Secondary hemostasis is the strengthening of that platelet plug. Coagulation factors synthesized by the liver are responsible for strengthening that weak platelet plug and converting that fibrinogen to fibrin. If the initial injury was caused by an exogenous occurrence (ie. cut with a knife), the extrinsic pathway would be elicited. If, however, the initial injury was endogenous (i.e. rupture of an atherosclerotic plaque), the intrinsic pathway would be activated. Both pathways lead to the conversion of that initial weak fibrinogen to a much stronger fibrin. Any issues in the coagulation pathway leads to bigger bleeding issues, most often presenting as hemarthroses (ie. Hemophilia A, B, etc), and excessive bleeding after trauma or surgery. PT or pTT time is prolonged depending on which pathway was activated.
Like I said before, this is overly simplified. Dr. Sattar on Pathoma does a great job explaining the two.
I hope this at least helps alleviate some of the confusion. 🙂