"People" is the normal plural word in English. "Persons" sounds wrong except in a few very formal contexts like legal documents. You can safely use "people" throughout this course and forget about "persons".
Ember is more of a general term - man, human, person. "Persons" sounds like a more artificial term, a legal entity, for which Hungarian has a better word: személy. You can find that word in many derived terms, like személyautó - passenger car, személyzet - staff, or the fun-to-say "személyi igazolvány" - personal identification (card).