There seems to be a discrepancy in the docs I'm trying to figure out and solve.
Most of the statuses are more explained here: https://clear.ml/docs/latest/docs/fundamentals/task/#task-states

Closed isn't yet.
Close is normally for manually closing a task: https://clear.ml/docs/latest/docs/references/sdk/task#close
You'll find more info here: https://clear.ml/docs/latest/docs/clearml_sdk/task_sdk/ and here: https://clear.ml/docs/latest/docs/guides/advanced/multiple_tasks_single_process