Platelets, also called thrombocytes (thromb- + -cyte, blood clot cell), are a component of blood whose function (along with the coagulation factors) is to stop bleeding by clumping and clotting blood vessel injuries.
Milk of the poppy is essentially the Westeros version of morphine. Maesters make it from crushed poppy flowers, and morphine and other opiate-based drugs are made from poppy plants. Indeed, the books' descriptions strongly suggest that the poppy is intended to be the real-world opium poppy (Papaver somniferum).
While the California poppy does contain some sedative alkaloids, it contains no real opium. The most common use of this herb is in diffusion for treating the various physical and psychological conditions including insomnia, bedwetting (incontinence), anxiety and nervous tension, particularly in children.