There is no such thing. There are Jupyter kernels. JupyterLab is just one of many UIs that speak the Jupyter protocol. Other examples include the original Jupyter notebook editor, VSCode Jupyter extension, and now Zasper.
I'm pretty sure Sage was always intended as a project that integrates the world, never "small footprint".
> There is no such thing.
A Web search reveals that the alternate term "Jupyter kernel," appears equally often. The terms are interchangeable.
> I'm pretty sure Sage was always intended as a project that integrates the world, never "small footprint".
A large install became true eventually, but it began as a small Python-based install, about 120 KB. Then people asked for extensions, and William Stein said "Yes".