In blood clotting disorders, the increased clotting time is attributed to issues in the coagulation cascade, while platelet disorders do not affect clotting time because platelets primarily function in the initial phase of hemostasis, forming a plug. Platelet activation is triggered by von Willebrand factor released from damaged blood vessels. The process of clot formation involves both primary hemostasis, where platelets aggregate, and secondary hemostasis, where a fibrin mesh stabilizes the clot. Prothrombin time (INR) specifically assesses the extrinsic coagulation pathway, indicating that both phases of hemostasis are essential for creating a stable blood clot. Red blood cells and platelets do indeed become trapped in the fibrin mesh, contributing to the overall structure of the blood clot.