> As with all ideas, everybody does their own version of it in practice.

Yes.

> Continuous integration (CI) is confusing.

At core, no. Not really. See the 1st paragraph of https://en.wikipedia.org/wiki/Continuous_integration :

> In software engineering, continuous integration (CI) is the practice of merging all developer working copies to a shared mainline several times a day.

So the 2 words are defined as follows:

Continuous: at least several times a day.

Integration: merge changes to master.

It's not a tool: it's a practice, a workflow that builds, tests and tools can help you do safely.

Some of these "CI Server" tools also support "build and test the branches" which is useful but is not CI. This is a common mistake.

See also: https://trunkbaseddevelopment.com/