Wouldn't running on the edge of the internet mean running on the devices that I see when I look around my house? It feel like this serverless thing is rather serverful, unless I've overlooked the part where users are running a node somewhere.
These days "edge" more commonly refers to the "edge of the cloud", i.e. still a datacenter, just not in us-east-1.
Serverless also does not mean no servers, it means no sysadmins.
Serverless is definitely a misnomer, but it means that you don't 'own' the server your thing is running on, there are some restrictions and you can't run anything you could on an actual VPS or hardware box. So in a way the server is abstracted away. You just use resources, but those could be anywhere, running on any node of the edge network.
Turns out, they meant installing modems in people's houses. Edge, it would seem, is a very versatile buzzword.
Serverless really should mean the client does the work, but it seems pretty equivalent to shared hosting. Dreamhost (and the shell account you used to get with an ISP!) was serverless before it was cool?
I'm aware that what they usually mean is significantly less interesting.