Hi Rick,
yes, your confusion is understandable and others have felt the same.
In this context, SAP does, indeed, refer to the set of huge application solutions that SAP AG sells.
The 'flagship' solution is probably Business Suite which large organisations use for managing their entire business - everything from payroll to stock control, CRM and ERP etc etc etc! These solution applications use a relational database as the repository - originally IBM's DB2, but now all the major DBMSs. In the SAP world, the database is just one 3rd party service component in the application. However, with the acquisition of Sybase, SAP now can provide a complete, all SAP, solution from end-to-end.
So, all those customers use the 'SAP on Sybase ASE' forum.
All the rest of the traditional Sybase database installations are considered "custom applications" - or, more specifically "NOT one of SAP applications".
It's a bit of a paradigm shift which takes a little bit of "getting used to".
I hope that helps, all the best,
- jon