No one else uses the term "cloud" like that

Broadly, "the cloud" is just someone else's computer. VPSes still fall into that definition. A lot of VPS providers describe themselves as "cloud" now too (eg one of the main hosts I use, HostHatch, describes themselves that way on their site).

If a single AWS EC2 or Lightsail server (which is essentially just a VPS in one region) is considered to be "in the cloud", why not a much cheaper, more powerful server with a different provider?

Nextcloud can be selfhosted

I use "my personal cloud" all the time. But that's just me.

I got another one. Self hosted but tunneled through cloudflare

I broadly agree that "cloud" has an awful lot of marketing fluff to it, as with many previous buzzwords in information technology.

However, I also think that there was legitimately a shift from a point in time where one got a physical box assigned to them to the point where VPSes started being a thing to something like AWS. A user really did become increasingly-decoupled from the actual physical hardware.

With a physical server, I care about the actual physical aspects of the machine.

With a VPS, I still have "a VPS". It's virtualized, yeah, but I don't normally deal with them dynamically.

With something like AWS, I'm thinking more in terms of spinning up and spinning down instances when needed.

I think that it's reasonable to want to describe that increasing abstraction in some way.

Is it a fundamental game-changer? In general, I don't think so. But was there a shift? Yeah, I think so.

And there might legitimately be some companies for which that is a game-changer, where the cost-efficiencies of being able to scale up dynamically to handle peak load on a service are so important that it permits their service to be viable at all.