Trends...
There has been a general positive trend over the last 15 years for designers to take on larger and larger scope of responsibilities within the product development process
15 years ago in the "Microsoft" era of formal software development, human-computer interaction, visual design, or information architecture were specific disciplines in design, and products were handed to specialists in these disciplines at formal points of the development process.
Since then, the trend has been to move away from specializations and allow designers to influence and direct broader and broader circles of scope in the development process. This has given rise to broader diciplines like UX design, as the diagram below shows:
(click to expand)

Some drivers for this trend:
- The promulgation of design thinking as a paradigm for end-to-end product development, not just "design phase" work.
- The incredible success of design-led companies like Apple, Dyson, Nest, and others, which has shown the business world how successful design-led development can be.
- The flattening of the development process by frameworks such as Agile and Lean, which leads to designers and other team members working more cross-functionally with larger scopes of responsibility.
- ...and so on.
Product design...
...is just another term, but it's also an almost predictable evolution/variant of User Experience. It represents the next enlargement of design scope, away from just user experience design towards an even broader mandate of design for an entire product.
This may include some or all of the bubbles in the diagram above: a product designer may work not only on crafting a user experience but also on functional ergonomics, technical design, marketing approach, and so forth.
Keep in mind that these terms are fuzzy, but fuzziness doesn't mean that there is no meaning to the term. When understood in the context of how a term evolves, it's easier to understand why it is being used, and what it's intended to communicate and differentiate.
Companies will use the term 'Product Designer' differently, but keep in mind that:
Some fuzziness in definition doesn't make a word unusable or useless (think of how fuzzy the meaning of the word F**k
really is, but yet it's still very useful =). There is value to the term 'Product Designer' because it communicates a differentiated scope of design responsibility.
Even if a Product Designer does not have a vastly broad scope of responsibilities for a particular company, there can still value to the company in using the term because it may communicate a commitment or aspiration to design-led product development.
Hope that helps.