How does the approach vary between a software product and a hybrid product (e.g. a router with embedded sftware)?

• Hybrid products are exponentially harder to build than pure software products. Software can be updated via the cloud, at any time and with any frequency but hardware cannot
• The form factor, the physical functionality, etc of a hybrid product need way more thought, user testing and context than the software. For instance, the physical components of the Tesla 3, the sensors, cameras, etc are paramount compared to the Maps, Apple Carplay integration or self-driving updates that can be done through the cloud 
• Context, background and living with the problem are the key for hybrid products. Only a Steve Jobs who has been living & breathing both Technology & Liberal Arts could have made the IMac, the iPod or the iPhone so user-friendly. But, a Steve Jobs as a visionary CEO alone isn't enough for such hybrid products. You also need a Today Fadell who has been living & breathing electonic products for 20+ years to launch the iPod and later the iPhone. 
• So, for people interested in hybrid products or teams builidng them, my reommendation would be to go deep and to live & breathe the problem before they are able to create a vision or build the product. And when creating the vision, over-index on the physical form & function since the first impression on users is very important and the physical form cannot be changed atleast for a year (or longer)

I think the biggest difference between crafting software vs. hybrid product vision statements comes down to scale. It's much faster to build, test, and learn with software product than products that touch hardware. With software, you can scale your product and customer base very quickly, whereas, hardware can take months, or even years to iterate and drive value. 

Over the course of my career, I've worked on mobile, web, and hybrid (mobile + hardware) products. A few years ago, I worked at Hudl Sports where I led product for Hudl Replay -- a video analysis tool for professional sports teams. The core product was an ipad app, but we were dependent on stadiums having accessible networking infrastructure to create a wired connection between our app and the IP cameras placed around the stadium, otherwise we had to creatively combine 3rd party hardware to establish a wireless connection. Since our customers traveled between cities, countries, and even continents, it was important for teams teams to have a reliable wirless network so that they could use Replay. 

Hudl Replay's product vision: Our goal is to help teams make data-driven decisions quickly with real-time analysis and instant replay. 

While the vision statement doesn't specifically mention time or scale, these were major considerations when crafting our goals. Product visions need to be aspirational, but they also need to be achievable. 

The software side of Hudl Replay made "helping teams make data-driven decisions" achievable given how quickly we could iterate on how our users interacted and worked with video data through our app. But, "real-time analysis and instant replay" was much more aspirational because we were entirely dependent on advancements in hardware. This goal was a much more long-term vision and would take longer to achieve. To make meaningful progress on this goal, we had to either build our own hardware or continue to rely on stringing together 3rd party hardware. Both paths were slow and expensive, but our team was excited about the problem and rallied together to find solutions together.