Hi ravl,
KDE uses so called "resources" as data source for PIM data. i.e. you can have 2 calenders one being a local KDE resource, one being a remote iCal resource.
You seem to
a) have to resources called "Default Kontact Resource" and
b) add new calender entries to both of these resources.
You may want to use only one of the resources - and delete the other one. I currently don't have KDE in front of me (unfortunately) but the place to look is the Control Center. There you can set up and administer your resources. I would suggest deleting one of the resources to have a clean setup with only one "Default Kontact Resource". The problem may be, that if you are already actively using one (or both) of the "Default Kontact Resource", you will obviously delete the data in that resource. :-/
Another thing to try is deactivating one of the resources in Kontact. Again, I don't know exactly where to do this, but I remember having a list with all defined resources, where you can check/uncheck the ones Kontact should use. Which also means: Display in Calender.
Hope this helps a bit.
Cheers,
Till