Freelance or self employed

That depends on how you translate these two terms to hungarian.

There is usually no real difference between a freelance worker (i.e. an independent contractor) and being self employed for the work you are offering. Freelance work is a subset of self employment. And you can do freelance work 9 to 5, or you can be employed and holding a full time job and do side freelance work. That is you may work 9 to 5 all week at a bank, but freelance editing poetry on the weekends -- the poetry freelance work is still self employment even if you have another full time job.

A better question is the difference between a freelancer and an entrepreneur. But if you follow the two links I provided, that answers it.

The real question is how is each taxed? You have provided no information about what type of work you want to do (for example, you can not be a freelance shop owner). So can not answer this question. To answer that: ask an accountant. Which you should do anyway, as tax rules change all the time.

I don't want to be a shop owner I just want to sell my work in no specific work category. As self employment in Hungary goes I must prove a school accreditation for a specific skill, I don't want to do that, so I was hoping that freelance work was different in that you don't have to show a specific skill set.