Python frameworks: Website/CMS vs application?
I don't know Pyramid at the time of writing so I'll answer the Django part, though I can imagine the answer to apply to Pyramid as well as the distinction between websites and web application is quite vague.
Django is suitable for both websites and web applications: you can create an informative website for your local library as well as an all-in web application with lots of interactive features. Django simply facilitates the creation of the backend of a web system. Both websites and web applications use databases, have caching and can have interactive parts with forms.
It's just that websites are usually just for informing the user (most sites out there) or interacting with others (such as forums). A web application is best described with some examples, such as webmail, administrative interfaces, Google Docs, etc; it serves as a replacement of a desktop application.
From a technical perspective, there's no clear cut thing that separates the world of websites from web applications, it's just a matter of what you create with your web framework.
To answer your question, Django is quite suitable for creating a database-driven web application as it supports multiple databases, caching, autmatic creation and handling of forms, etc. I can imagine Pyramid to be suitable as well but I can't answer that. It's good to explore your options.
I'm slightly confused on what is meant by a "web application". I.e. Django positions itself as  "a web framework" for the development of "web apps", quite similar to the description of Pyramid. What I'm looking for is a framework for an application that has a browser interface but is very database driven. In short: It's a system that should handle transaction and subscriptions. These transactions are registered through a web interface. The backend consists of XML/JSON feeds of these subscriptions/transactions and an administrative interface to generate statistics and reports. Quite similar to a ticketing/box office system.
Now: Is it a good decision to start out with something like Django/Pyramid even though they seem more focussed on the creation of "websites" rather than (scalable) input/output "applications". Is there any python framework that I'm better of using or are they perfectly suited for the kind of software that I'm describing? 
Any help would be greatly appreciated!