How should I communicate the specifics of cloud computing (as compared to other)

Question

A meeting today went well where I explained that cloud computing which one of the persons recognized was something else than a traditional RDBMS and I said that cloud computing is that everthing is software. It didn't seem like "Aha!" when I said it so I wonder what I should say. I thought the main specifics of cloud computing are integrated services, no traditional RDBMS and resources are allocated as software and payment model is pay per usage instead of pay per hardware. And/or should I stress the concept of PaaS i.e. that it is a platform?

Wikipedia says the distinction is between products and services but that we said about web services 15 years ago.

Thanks in advance for you answers