when sporozoites (mainly P Vivax and P Ovale) reach liver cells. They start multiplying to form merozoites, but some of the sporozoites invade liver cells and do not multiply rather go to sleep and called hypnozoite. In future ranging from days, to months, they can start multiplying and can produce merozoites which will lead to an episode of malaria. This is relapse.
Recrudescence, is when the parasite remains in the blood after the episode of malaria. This parasite in the blood, can anytime start multiplication and can cause malaria. This is more common with P falciparum but can happen with all forms of malaria parasites.
Reinfection, is of course a new infection of malaria. It is not possible to differentiate between these terms clinically. And PCR would be needed to confirm this.