The idea of "making money" is distinctly American.
“If you ask me to name the proudest distinction of Americans, I would choose [...] the fact that they were the people who created the phrase "to make money." No other language or nation had ever used these words before. [...] Americans were the first to understand that wealth has to be created.” Ayn Rand
To make a fortune means that you do something that creates value. The entrepreneur who starts a business and makes money has done so by creating value. Exactly, though in different degree, as the guy who takes a hot-dog cart to the top of a ski hill and sells his hot-dogs for $5 each.
That is, this is the case in a free market. In such situations, the money you get through trade is based on people's voluntary evaluations of the worth of various goods and services. So if you are doing something that other people believe is creating a value, you are creating value, making value, for them. And they are willing to give you value in return.
The most important graph in the world is the modest title of a Reason Magazine article. They show that world per-person income was essentially static for all of history until about the year 1800. At that time, capitalism was invented. World wealth began to expand exponentially. Not only was total wealth increasing, but wealth per person was increasing drastically. So much that, within the next generation we could well see the banishment of absolute poverty.
All of this has required the creation of vast new wealth. Making fortunes rather than just earning them. When the per-person income goes from less than $400/year to $28,000.year, there must be more money in existence.
So there is a very important distinction. To "earn a fortune" means to move that fortune from other people's bank accounts to your own. To "make a fortune" means to create it, to produce a fortune that did not exist previously.