Well, I guess you could say that's a form of patronage, but "arts patronage" as a concept is more of a general sponsorship of an artist in the hope that they will produce significant works (and maybe have some influence over their production), rather than a transactional relationship where you are paying for a specific piece.

Patronage seemed like a more formal thing though. They lived with the patron who would provide them a workshop, food and money. Their early days in a workshop seemed more like an employee at a business, not much different than today. The owner would have to go and find work and tap his network to find people who needed his businesses wares. He would hire employees, and they would complete jobs under his supervision. When Leonardo da Vinci was 14 and working at a workshop he was an employee of the workshop owner. It took him a long time to get a patron. He even sent letters to rich people trying to get their patronage by saying what he could do (and just like today, there was a bit of "fake it till you make" in those letters too :)