Human in the loop
Human in the loop means a person approves or decides before an action takes effect. Human on the loop means a person watches and can intervene. Vendors use both phrases loosely, so a page needs to say where the person sits, for which actions, and what happens if the person does not answer.
Definition
For containment the difference is practical. In the loop adds delay and a record of the decision. On the loop is faster and leaves the first wrong action to happen before anyone steps in.
Score the claim by detail. A named approver role, a tier and a timeout is a control. The words human review alone are a statement of intent.
Human in the loop in Swimlane's documentation
Swimlane's Turbine page says only that complex cases escalate to human-in-the-loop review, with no approval tiers, rollback or scope limit stated for actions. vendor claim swimlane.com, read
The example names a vendor and its own page. A vendor's use of Human in the loop may differ from the definition above; the rubric uses the definition on this page.