I'm a Leo - Leo rising, which is what the traditional definition of a Leo would be. The Sun sign being secondary to the Ascendant. But the description of a Leo you give, doesn't fit me either. I'm not loud or boisterous, though I do like to be the centre of attention. I'm certainly not the life and soul of the party but then I know I don't have to be. I do like showing off a bit, and I do like performing - I was a college lecturer for nearly 40 years and there's no better way of showing off, than teaching (provided you know the stuff). My Sun though is in Libra, it's Fall and so I'm a little shy and uncertain about myself.
Now don't be taken in by Sun Signs, unless you were born around dawn, they don't carry a lot of weight. Indeed those Sun Sign columns only work because the Sun is the easiest planet to predict in terms of it's placement at any one time of the year but it's not infallible, according to the dates given for those columns, I should be a Scorpio. Also those columns do assume you were born at or around dawn, and their predictions are based on that assumption. That's why they are largely wrong, though for some people they work very well.
You also need to look for your Ascendant (which requires you to know the time you were born) and at the positions of the Moon and the other seven visible planets (as these are the more important ones but by all means add in the outers if you want).
There are a number of ways you could try and assess your personality, the most frequent being the 'element count' for Modern Astrologers. but the Traditional Temperament calculation actually fits in better with psychology. Many of the theories of learning differences seem to be base on it (though the authors wouldn't admit that).
Ascendant, Moon and Sun are the basis of that approach and those are the three key personality indicators. You should be able to find those placements if you go to Astro.com and enter your natal details to get your own chart.
So the thing to pick up from this thread is that Sun Signs are but one of many factors that you need to identify begin to blend to get a more tempered and rounded view of your character.