A family of Microsoft word processing software products for creating web, email, and print documents.
I believe that "classic" and "premium" is mostly marketing vocabulary. Your screen shot indicates that the subscription products have "premium" versions of Word, Excel, PowerPoint and OneNote and that Office Home & Student has "classic" versions.
The practical difference is that the set of included Office programs is not necessarily the same. Home & Student does not include Outlook, for example.
Another practical difference is that the subscription products will receive new features, while the perpetual licenses will get bug fixes and security updates only.