People tend to use the word "design" very loosely when talking about product, but it's actually quite important to distinguish between the types of design (and their respective designers) when seeking to understand what someone means by the term in any given context, as well as how they apply to the overall product development process.
I tend to divide design into three main types: product, interface, and visual.
The goal of product design is to generate and prioritize functionality that could potentially deliver value to users in correspondence with the product's stated purpose, or to modify that stated purpose when no such functionality has sufficient potential.
A product designer spends their time mainly thinking about user flows and experiences, which is to say, how users ought to encounter the product at various points in their lifecycles, what they are enabled to do upon those encounters, and how that enablement provides users with additional value.
Such a design involves the least amount of illustration of the three types, but those in the form of low-resolution diagrams, flow charts, and even rough interfaces can help get the point across about how the functionality should work. Often the output of product design consists of verbal materials, such as outlines and essays that convey how the functionality will suit users' needs and psychological profiles.
A good product designer is aware that prioritization is key to their work because there isn't enough time or resources for all promising ideas and the ones with the most promise must be tackled first. And the product designer must continually map this product prioritization to the company's most pressing business objectives.
The goal of interface design is to translate the conceptual functionality conveyed by the product designer and articulate how the user actually experiences and manages to understand that functionality in the product, on a step-by-step basis.
If the product is a website, the focus is on arranging and defining various elements on each page that provides the user with information and input. If the product is a mobile application, then the medium is screen-by-screen, and if physical, its available materials.
The interface designer is most responsible for making the product as intuitively usable as possible so that the highest percentage of users derive the value promised by it. A good interface designer understands the constraints and opportunities afforded by their medium and plays the very empathetic role of envisioning and studying how people of all targeted backgrounds will learn (or fail to learn) how to use the product. And they're intent on ensuring that the interface elements come together in a cohesive whole that makes sense to users architecturally, delivering those elements as wireframes or other medium-resolution materials to the visual designer.
The goal of visual design is to ensure that the product conveys a sense of quality and elicits the proper emotional response from its users.
Visual design is the most aesthetic and subjective design type, but it's also the most immediately recognizable one. While visual designers take their cues from product and interface designers, they are responsible for crafting and delivering an ethos for the product. They spend most of their time making interface elements both attractive and appropriately toned so as to reinforce the purpose and value of the product for users, and a good visual designer knows how to make a product pleasurable without making assets that are overly conspicuous.
A visual designer spends the most time on detail, since they sit closest to the user's actual experience. And they deliver high-resolution images, animations or other user-ready elements that can be incorporated directly into the product.
Interrelation of types
These types can be treated as a hierarchy, in the sense that product design mainly informs interface design, and interface design mainly informs visual design. And as such, it's more important to execute successfully on the product design front than the other two, because decisions (both good and bad) made in that tier will cascade to the others. And it's hard, if not impossible, to make up for shortcomings in product design with amazing interface or visual design (or, likewise, to make up for poor interface design with a compelling visual design).
However, it's not desirable nor even theoretically possible to focus exclusively on product design without investing in the other two types. There's no way to actually manifest your product, let alone in a way that consumers find appealing, without spending a decent amount of time actually thinking through its interface and visual considerations and generating outputs from them. In an extreme yet feasible scenario, you could have barebones interface and visual design paired with solid product design and you might eek out traction in a marketplace, but you'll be making life a lot more difficult for yourself.
The practical question that startups often face, then, is how much attention to give each of these types of design, especially when their general hierarchy is recognized. Does interface design get 50% of the attention as product design, and does visual get 25% of that? Or do they all get roughly equal treatment, or some other division? The answer basically boils down to how much usability friction users can be expected to tolerate (on the interface front) and how central the notions of quality and emotion are to the product's value proposition (on the visual front) at any given release point.
If you are distributing a product (perhaps a business tool) to people who will likely find value from even a poor user interface and don't care much about how their tools look and feel, then you probably don't have to spend as much time on interface and visuals. But if your product (perhaps a game) needs to sway inexperienced and skeptical new users that it'll dependably provide them with emotional satisfaction, then you may want to make a thorough investment in all three design types. The consideration, therefore, is ultimately a marketing one.