[Izkata]

That's only the case where a usable generic core already exists. A great example where it didn't exist is python's "requests" library: https://requests.readthedocs.io/en/latest/

The example on the homepage is the "specific shell" - simple and easy to use, and by far the most common usage, but if you scroll down the table of contents on the API page (https://requests.readthedocs.io/en/latest/api/) you'll see sections titled "Lower-Level Classes" and "Lower-Lower-Level Classes" - that's the generic core, which the upper level is implemented in terms of.

[Twisol]

I like this example :) Another good example might be Git's distinction between "porcelain" and "plumbing"; the porcelain is implemented in terms of the plumbing, and gives a nicer* interface in terms of what people generally want to do with Git, but the plumbing is what actually does all the general, low-level stuff.

* opinions vary