The manifesto is governed by 4 Values and 12 Principles. Being Agile sticks when companies focus ground up starting with building the value system followed by practicing the values, doing some of the practices and hence getting the benefits. This is often referred as Inside Out Agility.
Under the Agile Umbrella, there are many methods. Scrum is a method, Kanban is another. There are many others as well. Within each of these methods, there are many practices.
In general Being Agile means, you are using one or more of the Agile frameworks but are surely following the four values and 12 principles as much as you can.
The recommended approach to go with imbibing Agility is something called Inside Out Agility. This focuses on making sustainable changes based on Culture, Structure, Agile Values and Principles and then following practices like Agile and Scrum. Most of the Agile transformation programs that follow an outside in Agility in order to gain the benefit of Agility. While the Inside out is not an easy path it has proven to be more successful than any other approach.