Service Workers (which are one of the core technologies behind the Progressive Web Apps label) go further than manifest files because they can deal with any kind of HTTP request (including e.g. calls to your REST API). Also, because they are code rather than static lists backed by hard-wired browser logic, you can implemnt any kind of caching strategy you want.

That being said, Progressive Web Apps is pretty much just an umbrella term useful for marketing several new and upcoming browser APIs (Service Workers being one of them) and not really a thing in itself.

You have a point; my impression is that, just like Ajax, more than a new technology/s, it defines a web development model, a certain class of webs sites that result from combining certain technologies in a certain way that makes them have certain characteristics that make them distinctive.

There was the Application Cache (which used a manifest), but it was removed and replaced by service workers.