There would still be economic differences between different types of businesspeople, and different business types would still require different amounts of initial training and on-going practice.
For example, if my desire was to create the best brain surgery business in the world, I'd need to invest in a lot of training for myself (this could be a time investment, assuming that all education opportunities are open to all), in getting contracts with skilled anaesthetists, surgical nurses, operating theatre equipment manufacturers, cleaners, receptionists, and logistics providers (I need blood delivered regularly, therefore I need a reliable transport company, with a reliable storage system, and related maintenance), in getting people to use my brain surgery business (marketing/advertising) and in ensuring that there is post-surgical support for my patients. That's a lot of effort, especially when I can't (due to lack of interest from other people) employ them to do specific jobs. I'd have to pay the best rates, and offer the best standards to keep them, else someone else could come up with a better contract for them.
On the other hand, if I want to be a freelance artist, I need some materials, and possibly some way to show off my work, but essentially it's just me. The materials might need third party support, but I could work with found materials (e.g. wood from forests, rubbish, mud) and still do OK if people like my work.
In both cases, basic life requirements such as somewhere to live, and food and drink are essentially the same.
However, the artist can sell a lot of art works. They are constrained essentially by the number of people they can find who want to buy what they create, and the time it takes to create their works. The price they get for their works doesn't necessarily correspond to the time or material cost. If people like what they create, they can be rich and successful. If people don't, they will be poor and lacking in basics.
The brain surgeon can only operate on people who need brain surgery. There are presumably a limited number of these, so this is essentially a low demand occupation, but when you need a brain surgeon, you're willing to pay whatever it takes. The price they get for their work probably starts higher than the artist can handle, but the expenses are a lot more too. If there are lots of people needing brain surgery, they will be rich and successful, but also really busy, so possibly lacking time to enjoy their income. If there are no people requiring their services, they won't be rich. They might even be in debt to people they have contracts with.
You would also have some problems in this society. There are some businesses that can't work without multiple people involved, and there are some jobs that don't necessarily result in a direct gain for the worker. An example would be an airline pilot - they can fly the plane themselves, but how would they get a plane in the first place? The initial investment would require contracting with 100s or 1000s of people to build it, then it's totally useless unless you have other people determined to build the best airport business in the world, people determined to drill oil, people determined to refine the oil to fuel, people determined to transport the oil to the airports, people determined to operate air traffic control towers (would you have a contract with each individual? If not, what if you have a contract with Alice, and Bob is controlling the rest of the planes in the airspace you're in?) and so on.