There is no "desktop online" version. There is Desktop and then there is Online. He might be referring to the downloadable "app" to run QB faster from outside any specific browser - but apparently with little fanfare that app "has expired" and the current only way to access QBO is through a browser (even from a phone)
UPDATE: the app is still around, although I went to the intuit app store and could not find it, but maybe this is what the boss saw. https://quickbooks.intuit.com/learn-support/en-us/download-products/quickbooks-app-for-windows-and-m...
It never worked properly in my experience and was a disaster attempting to use it with QBOA the accountant version but every time we logged in we were presented with a button to push that said words to the effect like never have to log in again and work 30% faster all from your desktop.
The online versions of QB are all accessed through an internet browser of your choice. Certain things work better in Chrome but certain tasks (like exporting ONline to Desktop version) require IE
