In years past, software was purchased upfront and outright so you owned the license. That is the perpetual license model where you paid upfront and then a smaller annual fee to allow you to receive the latest versions. If you stopped paying the annual fee, you could no longer download the latest version but could continue using the original version you had. In the subscription model, which most publishers are now supporting, means you pay a fee each month or each year and for that you get access to use the software. If you don't pay, after a period of time, the software is disabled and you might get the opportunity to see your information but not add any more.
Perpetual or Subscription usually refers to the same features and functions, same installation (whether on premise or in the cloud) but the software license is different.