Hi Kjetil Lønne , Thanks for posting your query on Microsoft Q&A.
I can see how the two can be very confusing as they seem very similar, from one look at the definition.
The main difference between the two is that -
Agility focuses on the speed and ease of allocating and deallocating resources. This allows for vast amounts of computing resources to be provisioned in a matter of minutes, making it easier for you to respond to changing business needs.
Whereas Elasticity focuses on the ability to automatically scale resources based on demand. This helps you to optimize your resources and reduce costs, while still ensuring that your applications have the resources they need to run smoothly.
I hope this helps clarify the difference between Agility and Elasticity in Azure cloud services for you.
Let me know if you have any other questions in the "comments" and I would be happy to answer.
If this helped, please 'Accept Answer' so that it can help others in the community.