Taking the phrases exactly.....

I don't have money = I am not a rich man. Money is something I do not have.

I am broke = At present, I have no money.

We can make a small change:

I don't have money on me = I have no money in my wallet or on my person at this moment (but I do have money in a bank account or at home)

I don't have the money = I cannot afford it; it is too expensive for me

I would like to take a vacation but I don't have the money.

Could you pay for lunch? I'll pay you back tonight. I left my wallet back in the hotel room and don't have any money on me.

After paying for food and rent and the train to work, by the end of the month I'm broke.

My family lived on a very small farm. I left our small village to find work in the city, where I drive a taxi. I don't have money.

My friend at school inherited a fortune from his grandfather. But my grandparents worked every day of their lives, and just managed to scrape by. They didn't have money and my parents didn't have money and I don't have money.