Python frameworks: Website/CMS vs application?
I believe that at this point you might want to think more about the overall architecture of your application rather than frameworks. For Example

Single Tier - Just a simple webapp, using simple file or object storage
Two Tier - Webapp + Relational Database. The webapp contains the presentation logic + business logic using MVC principles
Three Tier - Webapp + Middle Tier + Relation Database. In this setting, the Middle Tier will basically contain all the business & processing logic. The Webapp is then just a presentation layer

Once you decide the architecture, you can then start thinking about which framework to use for each of the component of the architecture.
I believe progressing this way will be less confusing and will give clarity of thought.
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!