Hello! the difference is that "essi" is the SUBJECT of the 3rd plural person while "loro" is the DIRECT OBJECT. The problem is that "essi" is a bit weird and not very used in the italian vocabulary so what italians do is using "loro" also for subjects, even if it's not grammatically correct.
Right way to use the pronouns:
ESSI studiano insieme ogni martedì.
Giovanni guarda LORO che studiano.
Wrong way:
Loro giocano a calcio.
Hope I was clear and come on my profile to book a lesson together!