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?