The AEM CIF Connector provides a number of authoring features, like product picker/category picker that is nicely integrated with the existing AEM Sites editing environment. In addition to the connector there is also CIF Core Components that can be used as is with CSS/branding updates or extended just like regular Core Components. Everything is open sourced and new versions/updates are rolled out fairly regularly. The Connector and CIF Core Components are designed to be used with any Commerce backend however the support for Magento is the most mature. Support for a 3rd party integration is available via Adobe I/O runtime, but will require custom coding (although some starter reference implementation is available)
Support is available for AEM as a Cloud Service, 6.5 and 6.4.4. In terms of headless vs. who owns the glass, AEM CIF can be thought of as AEM owning the glass with a a headless commerce backend. The AEM authoring experience is the biggest value-add from an AEM CIF side. The ability for marketers to customize Product detail pages, category landing pages and coordinate content/offers with an in-line authoring experience is very attractive. AEM CIF follows the same design patterns as traditional Sites, so if personas are already familiar with Sites (be it developers or authors) then it is an easy transition. Additional links to read more:
https://www.adobe.io/apis/experiencecloud/commerce-integration-framework/integrations.html#!AdobeDoc...
https://docs.adobe.com/content/help/en/experience-manager-cloud-service/commerce/overview.html
https://github.com/adobe/aem-core-cif-components
https://github.com/adobe/commerce-cif-connector
https://github.com/adobe/aem-cif-guides-venia
