Are there any real differences between Office 2010 (the perpetual license retail product) and the 2010 version of Office 365 (the subscription model)?
You've got it right, one of them is actually a real retail product of the now age-old (an ancient) Microsoft Office sold to people with lifetime license (or some licenses), and the other is part of a service offered by Microsoft to use the latest version of Microsoft Office as pre paid service. So, one is product, the other is service, most correctly one part of Microsoft 365 service.