I agree, but that's colo/on-prem. Not a private cloud, which is typically just some allocation of dedicated resources from a public cloud.

Huh. I always thought of "private cloud" as meaning "my own server", not a carveout on a public cloud. I learned something new today.

How does such a "private cloud" differ from using the "public cloud"? The two seem identical to me.

Well, it can. The definition of public vs. private cloud depends entirely on who is selling it to you.

It's not even a binary at many of the large providers: you can have dedicated servers ("my own server") in a public cloud at AWS, for example.

Personally, I keep it simple. If I can physically hit a box and no-one can get mad at me, then it's private and mine.