The sun in a birth chart represents your core being. Its placement, and its aspects, give us a very general sense of what you need most for your own personal growth. In other words, what you need to be happy.
Sun sign is part of this picture. But so is the house of the sun. If you are, say, a Gemini, your Gemini-ness will manifest quite differently if your sun is in the secretive twelfth house, than if it’s in the highly visible tenth. Still differently if it’s in the very Gemini-like third house. And that only covers a quarter of the possible house placements.
Aspects can modify the sun’s manifestation as much or more than house placement. A sun in tight conjunction to Mars gives us one kind of message. Square the moon, another. Opposition to Neptune tells us yet something else. And, of course, any two or all three of those aspects could exist in the same chart. As can seemingly infinite other combinations.
But even that says little about personality. Your personality is shaped by your personal growth and life experiences, which in turn correspond with the messages in your birth chart. But how it’s shaped depends on you. People with highly similar birth charts can, and often do, have very different personalities. That’s because they each respond in a different way to the birth chart’s messages.
The differences are even greater when we consider people who have the same sun sign but not much else in common in their birth charts. In those cases, each individual has the same basic message in their sun sign, but they are receiving very different impulses from the house placement of their sun, its aspects, and the placements of their other planets. They may be as similar to each other as a pair of jeans is to a window curtain: both are made from cloth, but the resemblance mostly ends there.
Your sun sign is not who you are. It’s how you become what you become. And even the how can have different manifestations.