What's the difference between the shell and a terminal?

Not the set up for a joke.

Both are programs, both facilitate interacting with a computer operating system. It’s easy to use both without having to think about what distinguishes the one from the other, so what is the difference?

The Shell, so named for being the outermost layer around an operating system, is the interface through which an operating system exposes its functions.

There are two types of shell: command-line shells, and graphical shells.

A terminal, or terminal emulator to give it its full name, is a program that provides access to a text-terminal/command-line interface.

Thus an operating system can expose a shell directly, or through a graphical shell can present a terminal emulator window through which you can interact with the OS’ command-line shell.

See also: Shells are Two Things by Fernando Borretti

And once you’re at the shell, you have access to the exquisite power of shell pipelines,

Shell pipelines are not things of static beauty, they are interactive dialogs with the UNIX shell, chatting with it to come up [with] ad-hoc ways of gluing together tools to the get at the bespoke outcomes we want.
Manav Rathi, On the useful use of cat, 2024