The kanji and the word are exactly the same. That means they share meanings as well.
When you have the ambition to do something, it feels like you're pointing at it with your heart. To say "heart pointing" in Japanese, you could say 心ざし (こころざし), which is how this word was written in classical Japanese. In modern Japanese it's always 志, but the reading is exactly the same. Now get out there and heart point to your dreams!
I hope you will grow up with big ambitions.
I have decided to live a life of rich ambitions.
Viet has high aspirations and is steadily making his dreams come true.