GRE (Graduate Record Examination) is equivalent to Jamb for doing graduate studies. It’s an entrance exam for graduate studies (masters or PHD).
toefl (Test of English as a Foreign Language) is an English proficiency test. It’s mostly required of non-native speakers of the English Language, when they want to study abroad.
Most graduate programs require the toefl for admissions but you have to check if the program you are going for requires GRE (or any other entrance exam like GMAT) or not.