I'm not sure if identity and personality are substantially different.
behaviour
capabilities
beliefs
values
identity
Each level structures the level before it.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?
My personality enjoys the meditative aspect of long distance sports. People who observe these behaviors call me a runner (identity). I don’t consider myself a runner but cant argue that when you see me running for 2 hours, saying “hey look a runner” is a reasonable thing to say.