I believe that is (or at least was) true at Google - although from what I knew of the role, it sounded like it also covered what I would consider project management. (I think I would often consider program mangement to be coordinating/managing across multiple projects as part of a broader program of work, but I don't think that was what Google meant by that title.)

The distinction between a program, project, and product managers seems to be mostly dependent on the company you work at.

All the various "PMs" at companies I've worked for have done largely the same jobs that are some mix of managing the project and figuring out new features for the product.