For inbound bundles, the parent action is the container and the member actions are the individual offers inside it. In Pega CDH, inbound bundles are defined by creating a parent Action and associated member Actions, and those are then bundled together for presentation to the customer.
Bundling is typically resolved in the decisioning layer / strategy output, not just at the UI. The bundled offer is assembled from the parent and its member actions, and the bundle can then be delivered to inbound channels such as agent-assisted or web self-service. For fixed bundles, the parent action defines the bundle, and the member offers are associated through the bundle configuration. Pega’s documentation for inbound bundles says to define a parent Action and member Actions and associate them with corresponding treatments
On a web page, the bundle is usually shown as a single customer-facing offer tile or bundle card, with the member offers displayed inside or beneath it as included products/services. So the end user usually does not see separate parent/member actions as independent offers unless the channel is designed that way.
When the response is captured, usually the it is captured against the parent bundle action because that is the customer-facing offer they accepted or rejected.