This is an interesting question and it relates to many of the things we use today. In many cases we do not own software, cell phones, videos and many other "licensed" products, we have simply paid to access them.
On one hand it often means having access to the newest things, on the other it means that the owner can revoke our access and we can not sell the item or its derivative.
With many FIAT currencies, we do not own them either, we are borrowing them from the government and have the right to exchange the borrowed notes, coins or digital value. In that sense, we really don't own anything. We used borrowed money to access it.
So I would say access is more common than ownership, but ownership is greater because control is greater than access.
I started noticing this cropping up as a "millennial" trend. From Netflix to Airbnb to Uber, the physical good, owned only in illusion (financed) seems to be vaporizing and with it the status those material possessions have always bestowed upon the owner. And in the end, we really don't own anything, we are borrowing time in a shared experience.