Are talking about rich versus poor in terms of money? Or what you have in life that cannot be purchased with money? I am going to address rich with money, but I realize that money isn't the only way to be rich.
If you had lots of money, so much money that you didn't have to work and could own really nice cars and live in larger homes, you wouldn't call yourself rich. You would call yourself wealthy. A wealthy man, the father of two former students schooled me about these terms. He had Porsche's, lived in a very large 3 story home with maid's quarters (not his wife), and multiple lots. He definitely had room for a swimming pool, but did not have one.
Is it okay that I address your question in terms of the word wealth? I realize you are probably not talking about money.
In my opinion, based on conversations with my family who have owned and lived off the land, wealth means owning land and property. It can be homes or land. No one who lives on the streets has wealth. No one who is a renter their whole life is wealthy. When you have wealth, you also have some power and some control over your life that others may not have. Owning property can give you power.
Depending upon your interests, you and your family might have a good education--medical, legal, MBA, engineering. You might have had a private school education growing up, but the part of being wealthy can and often does end when you are on your own as an adult.
You might be someone who has good self-discipline to keep moving forward with the accumulation of wealth, instead of finding ways to spend your money. This might be through investments, running some sort of business or businesses. Poor people have many wants that they will spend their money on soon after it comes to them, whether it is a necessity or not.