Cloud kicks has a muli-screen flow its call center agents use when handling inbound service desk calls. At one of the steps in the flow, the agents should be presented with a list of order number…

An invocable method is the mechanism to call Apex from a Flow, but it doesn't describe the specific implementation for external system integration; the actual logic for a REST callout would reside *within* such a method.

An Apex class can be written to make outbound REST API callouts to external systems, such as an order management system, to retrieve data in real-time. This class can then be exposed to the Flow using an @InvocableMethod annotation, allowing the Flow to execute the callout and process the returned data for display.

An outbound message is used to send data from Salesforce to an external system based on record changes, not for actively retrieving real-time data from an external system.

While an Apex controller contains business logic, an 'Apex REST class' (interpreted as an Apex class making REST callouts) is the specific construct for this type of external service integration.