In business, it is well-known that anything that you call a product or service should solve a customer's pain points, needs or problem areas.
Before the information revolution, the term "product" are normally associated to tangible or physical things (think manufacturing goods or items).
Focusing on the digital world, my own definition of software products are:
application software or software -- mostly run on Desktop
website -- mostly web pages that are combined together
web application -- think Desktop software; but it runs on the web
platform -- the most complicated to build and spans multiple use cases -- may host an app or service or may provide you development tools so you can build something on their development platform
There are other types of software products such as drivers, firmware, etc. but it is out of scope of this post.