In my experience, it does vary.
I think, if you were to look at the models of product management and theory, then the marketing piece would be in there, and it should, as a holistic view of managing the product.
In practice, different companies execute it differently, depending on how the company is organized, what their industry structure might be like, whether the product is THE only product in the company, one of a couple, or one of many, etc. Which requires you to study the job descriptions and see what is written and not written into them. And whether product management is an established, or newer function.
Of course, I suggest that you keep exploring this as you investigate your path and options.