The Agile Manifesto was a reaction against heavyweight methodologies that were popular, yet crippling software projects from actually doing what they needed to do – create software that helped the customer!
Agile’s values (Agile Manifesto) & Agile Principles work because of the science behind Lean Product Development and so you'll see a lot of similar themes repeated in Agile.
Any project that follows the Agile Manifesto & Agile Principles can rightly be considered to be Agile. That said, there are definitely preferred practices that are common for Agile Delivery Teams to follow in order to achieve agility. Most commonly:
Agile teams work differently from Command-and-Control Management bureaucracies. They are largely self-governing: