Supervisors and Dynamic Supervisors : Do they interoperate?

Error message does not help as it returns {:error, {:invalid_child_spec, child_spec}} while the spec is valid, but the issue stems from the interop issue.

If it existed, a DynamicSupervisor.supervisor() type would have the same values as Supervisor.supervisor() - the possible values are ways to identify an supervisor process, not specific details about the kind of process.

To use a telecom analogy, the type says “this is what patterns of numbers you can dial to reach a remote phone” but doesn’t specify who answers.

Many of the functions in the two modules are nearly identical, but handle arguments a little differently - for instance, start_child:

https://github.com/elixir-lang/elixir/blob/v1.13.4/lib/elixir/lib/supervisor.ex#L821-L837

vs

https://github.com/elixir-lang/elixir/blob/v1.13.4/lib/elixir/lib/dynamic_supervisor.ex#L317-L330

Both ultimately result in a GenServer.call with a message shaped like {:start_child, child_spec}.

Yes, but internally, the child spec for DynamicSupervisor is a five-element tuple, and for Supervisor is like the old erlang child spec, with 6 elements IIRC.
The error is cryptic, it says ‘:invalid_child_spec’ and if you call the same function with the same child spec but your suppervisor goes to the local supervisor the the function works fine, since the chld spec was valid.

Having a new type is a way to document that DynamicSupervisor functions expect a DynamicSupervisor and not a regular Supervisor.