The key differences are how you will work and the mindset and practices you will align to when working.
We need to align with the Agile mindset to work in the Agile way. The traditional waterfall mindset emphasizes processes and tools, comprehensive documentation, contract negotiations, and detailed planning. The Agile mindset emphasizes individual interaction over process and tools, working product over comprehensive documentation, customer collaboration over contract negotiations, and responding to change over having a detailed plan.
When we work with a different mindset, we will change our practices to align with it. We will use frameworks such as Scrum and Kanban to help break down corporate silos to enable collaboration. We will establish a working cadence and use a frequent show-and-tell technique to receive customer feedback.
The result is a modern and advanced way of running projects and developing products, with a greater chance of success.