On the other hand you’re not out there writing slam pieces on project managers, so I don’t think your lack of clarity around these terms is causing anyone any heartburn. And yeah these terms are a little under-differentiated in some shops. How I learned it [0]:
Project manager handles a discrete undertaking with a beginning and an end that falls outside whatever your org considers “ongoing operations.”
Program manager handles a portfolio of interrelated projects. If a lot of projects are failing and you want a single throat to choke, the program manager might be a good person to replace.
Product manager seems like it could be interpreted as kind of like a program manager (for a large, complex set of inter related projects) or a project manager (if there’s only one project) except that the organization’s ongoing operations include the creation and development of the product, instead of the product being a single event/discrete undertaking.
Source: read PMBOK decades ago
[0]: maybe others who learned differently can chime in? Doesn’t seem like this terminology is universal.