Change, Endurance, and Personal Identities
In a very real sense, I am not the same person I was five years ago. Today, I am a young adult. Then, I was a high school boy. His concerns, desires, and beliefs are not the same as mine. We don't share the same friends or acquaintances, my personality is not the same as his. Much that was central to his identity no longer exists. Even our bodies are not the same: many of his cells have died and been replaced by new ones.
And I am not the same man I will be in five or fifty years either (supposing Iive that long). Their bodies, minds, and circumstances will all have changed—my sense of subjective continuity might even be destroyed by a brain injury or dementia.
But, in another sense, I am surely the same person I was and will be. We have a unique reason to care about our future selves, we must make amends for wrongs we committed in the past. If my parents become demented, I will still have an obligation to take care of them.
These are two separate concepts, both called "personal identity." The former is our ephemeral sense of self, and it will decay long before we do. The later is our enduring self. This is what philosophers usually mean when they discuss "personal identity," and its nature will vary with your philosophical views—a brain region, a stream of psychological continuity, a Cartesian intellect.
I do not know if many other people can identify, but naming and clarifying this distinction has been helpful for me. It's given me a sense of stability in a world where everything changes, especially myself.