Are there terms to distinguish between the different levels of Drupal Core?
I'm not aware of any official definition of the various levels.

I will however, referring to your suggestions, explain a bit about what levels there are.


The Drupal Kernel is actually a component in Drupal 8, which is a Symfony Kernel
"Deep Core Modules" could be the include files that are not even modules. Some files, for example database.inc, bootstrap.inc and module.inc are so fundamental that core cannot function without them. (There are some more .inc files however that reasonably could become modules, I don't know why they are not)
Core modules then, core parts that are written in the same style as contrib modules, but are still so fundamental that core wouldn't work without them. There's a system module that manages a lot of low level administrative functionality. The node module is (in D7) still required. Field sql storage cannot be turned of either.
Outer Core Modules, are all the other things that are shipped with core because they are commonly used, but not necessary for Drupal to function. The forum, taxonomy terms, the user interface for the field system etc.


Again, I'm not familiar with any official terminology, other than all of it being "Core". When people work on core, I only hear references to the individual "components" of core, as specific in the Drupal issue queue.

When I hear "actual core", I think of levels 1 - 3.