where to start....
on SMT , you summon ''Demons'' to fight with you ,they appear as different party members, and normally are obtainable through fusion or recruiting during battles.
every demon has a ''Personality'': which is about the same as their mythological origins, such as Fenrir, Lucifer,Beelzebub and Thor, they can even be real-world people like Emperor Caesar and Jeanne D´arc/Joan of Arc, they will always say something about their story and stuff like that.
But, in Persona , instead of the Sidekick Demons, you have ''manifestations of One´s Psyche'', In persona 3 - 4, every character, except the main character(obviously), has only one Persona, normally reflecting their Personalities.
''Persona'' and ''Demons'' are just Given names, most Personas are Demons from SMT , and Vice-versa.
you can look for more examples on this page:
http://megamitensei.wikia.com/wiki/Persona_(Series)