I am not sure I understand dynamism. Perhaps dynamic is a better word.
Dynamic is a state of change. Interactive is an action that produces a result. The two are obviously interconnected.
Your description is more or less correct. Dynamic represent the back-end. Interactive represent the front end.
By back end, it means processing are done behind the screen, without the user aware of the process.
The front end, is of course what the user see on the screen and 'interact' with.
For me, back end means PHP, a web programming language hosted on the server. It is more powerful than AJAX & JSON because it can interact with a database.
AJAX and JSON is restricted by design to run without any storage. It is meant for use in the browser to bring better interaction for the user. So, it is able to change the display, but everything is wiped out once the browser closes. A sandbox environment of some sort. Of course HTML5 changes that. HTML5 allow storage to be set at the user computer. If I am correct, once you close the browser, the storage also disappears. Think of it like a temporary cache. Which is why I put it as front-end and related to interactivity, not dynamic.
Hope that helps. Good luck!