Trump University was built around the brand of Donald Trump rather than academic excellence. It was a for-profit institution driven by generating profit. This is contrary to the academic background a non-profit university brings that is research intensive and focused on academic achievement. It is not to say that nobody gained value from attending Trump University but they likely did not receive the substance that an academically rich university would provide.
Yes, Donald Trump ran a school that duped its students. He compelled them to spend their savings on an "Entrepreneur Initiative" containing little content and empty promises. Is it illegal? We can't be sure until we have more data. We can say with certainty that it was fake, however.
"University" has a comfortingly intellectual ring to it, providing students with a sense of security in their investment, regardless of whether or not accreditation for the school exists. Trump used clever marketing schemes to convince prospective students to buy into the program, and to keep on spending.
Donald Trump ran a fake school. He opened Trump University in 2005. This was a for-profit university. He is being sued by former students and the New York State Attorney General. The suit alleges professors were not hand picked by Trump, as he was supposed to do. A trial court found trump personally liable for running an unlicensed school in a suit brought by New York State.
Trump is for sure an entrepreneur. He ran a business teaching people his secret to success. There are many people out there who do the same thing. You can call it a school, but it was a business. Learning can occur in many ways. If a customer wants to pay for advice from a person who has achieved what they want, there is no problem with that. Trump just had to market his school in a different way to not mislead the public. University is prestigious, school is not. It is easier to ask forgiveness than to get permission.