Type tests are partly what you assume, Load, soak, stress… the conceptual type of test you are implementing.
They have nothing to see with the executor though. No parenting, nothing. The executor is just the technical way to implement that test, whichever it is.
The default executor, I believe it is the Rampìng VU executor.
As joslat said, the “types” (load, soak, stress) are general conceptual types of performance tests that you might run. Those terms are completely independent of the tool itself.
Scenarios/executors are k6’s implementation to design the workflow being executed by the performance test in order to meet the criteria for the system being tested. A test may use any number of different executors depending on the workflow you are attempting to model.
As far as the default, if you do not provide any kind of configuration (whether using scenarios/executors, or the top level options such as vus, iterations, stages, duration, etc.), k6 will simply execute a single iteration of your test script with one user.
Of note, the top level options (which were present prior to the introduction of scenarios/executors in k6 v0.27.0) will be implicitly converted at runtime into a single-scenario test using the appropriate executor: