This is actually a new product using the old product name.

Yes. The product/service now known as Azure DevOps was originally called the Team Foundation Service, then Visual Studio Online, then Visual Studio Team Services, and now it's Azure DevOps. This Visual Studio Online is a new product/service.

One of these years they'll get the name right! I typically refer to it as "Whatever they're calling VSTS this week"

That’s correct.

At Google it's very common to use the internal web IDE called CIDER.

At Amazon, some people use AWS Cloud 9 as their editor of choice but it's pretty uncommon in my neck of the woods.

Is the internal IDE based on this https://github.com/jordoncm/cider ?

No idea, but I'd guess not.

We call Visual Studio Online a “companion” web editor, because we expect it to be mostly useful for quick tasks, or on-the-go access. We believe that the bulk of your work will still happen in an editor (which is why we’re building remote support in VS and VS Code), but a web-based client can be really convenient for things like quick edits, or Live Share sessions.