I guess edge is just a buzzword, maybe it is like a metaphor; if you think of the internet as a sphere users reach to for content, something being on the edge means you don't have to reach that hard, it's right there on top. Or maybe it means close to the edge, close to end-user devices.
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.
Right after CenturyLink rebranded to Lumen, but before I heard about it, I clicked a buzzword-laden link looking for people involved in "Edge Computing". I had been writing vehicle traffic controller firmware and thought "hey, I guess I'm doing edge computing--out here at the curb--maybe I should check this out."
Turns out, they meant installing modems in people's houses. Edge, it would seem, is a very versatile buzzword.
I feel like Edge is more acceptable; running at a PoP is close to the edge; running inside an ISP network is even closer; it's not really achievable, but running in ISP managed modems or cellular base stations is pretty much the limit of plausible Edge computing.
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?
When I hear "Edge" I imagine that it keeps working if you remove the ISP (e.g. it'll still talk to with other stuff on the LAN) but it works better when the internet is available. Like bit torrent.
I'm aware that what they usually mean is significantly less interesting.
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.