How are owners of big business empires called

Magnates, Moguls, Tycoons

These are the names commonly used, especially by journalists, to refer to people in charge of big business empires. These words often combine as follows:

media
press                          MAGNATE
shipping 
oil


movie
media                        MOGUL
shipping 


property
software               TYCOON


Among famous magnates you will find for example:  Henry Ford, Martha Stewart, George Soros, Andrew Carnegie, and many more.

Among richest movie moguls you will find for example: George Lucas, Steven Spielberg, Thomas Tull, James Cameron, and others.

And of course, most famous tech tycoons are Bill Gates, Mark Zuckerberg, Jeff Bezos, and others.