Identity is a collection of beliefs (I identify as X, often context-free/in all contexts), whereas personality is a collection of functions (I behave like X, usually in a given context).
behaviour
capabilities
beliefs
values
identity
It is quite possible for one person to have certain beliefs, and have those beliefs be part of their identity, while another has the same beliefs but does not have them as part of their identity.
Why would anyone over the age of 7 or so have beliefs? Are you all so good at life that you play it with a handicap, like some expert golfer slumming it with us losers?