I'd divide it differently: waterfall is process based, Agile is outcome based. You know you're doing Agile right when you have code in front of a user and they

I'd divide it differently: waterfall is process based, Agile is outcome based. You know you're doing Agile right when you have code in front of a user and they're telling you what they like and don't like and what they wish they could do but can't and are connecting your product to their goals and stories. Agile gives you some structure and best practices around shipping early and often, communicating ina particular way with stakeholders and your team, and measuring progress. But ultimately everything - ceremonies, comms, management, PM software - is subordinate to the idea of "a user using your product to do the things the product is designed to do."