Financial stability is basically tailored to one's understanding and perception about finance and what their satisfaction about it means. so, to some people, stability in finance means to afford their daily needs while to others, it means the ability to afford their life's wants and to some it simply means ability to reach out to a larger multitude with financial challenges and others it means their ability to live a luxurious lifestyle.
I could never had said it more simpler, your definition of financial stability is very simple as what you said is actually the whole concept of it because some humans need to feel financial satisfied once they can carter for children while others feel having that finance that can lead you to provide an extensive hand is simply the satisfaction they want, well as for me I define it to be a state where your needs and wants is easily accessible and to some extent without fear of losing it all
This is what I was talking about. It will always depend on our own understanding and situations. While others see financial stability as being independent from their parents' financial help, other may view it as being able to buy everything they set their eyes on without worrying if they'll have the money to survive the next day. We all have different backgrounds and community that influences the way we see and understand things such as financial independence.