I like this::
Stubbby 10 points 2 days ago*
Embedded is not what you described.
Embedded is rewriting a portion of a TCP/IP stack on an RTOS MCU in order to communicate with a random switch thats on a board. After 2 weeks of dissecting signals with 5 probes you finally find out you just need to change 3 - 4 lines in handshake response that ignores the speed negotiation and hardcode the speed.
It takes a special mindset to work on something for weeks as you sit at 0% progress until randomly you hit 100%.
Its like fishing but almost all fish in the pond got eaten and there is only one big fish left and you never know when or if it takes your bait. Some people enjoy it (I consider them masochists).
This:
We built it from the ground up; the physical design of the enclosure, the printed circuit board, the firmware that ran on that board, and the app that accompanied it on your phone. It was honestly exhilarating. I really cared about that project.
is not embedded.
You are describing a startup.
EDIT:
Forgot to add, there are web developers at startups that do embedded work and embedded developers that design websites.