The accounts are different. I believe that the problem in your case is that in relation to Start Menu, Desktop and a couple more of things there is something else (not exactly an account) called "All users". If you go to your Documents and Settings folder (normally c:\Documents and Settings) you will see the folder corresponding to "All users". In this folder, icons and stuff are stored which will be visible to all the computer users. What you probably have done is to delete items from this folder, therefore you now don't see them anymore in any account.
To do what you wanted to do, the easiest way would have been to log in as administrator, go to documents and settings (with the explorer)-> your daugther account folder-> Desktop, delete what you wanted from there. Or if the items were in "All users" you should have moved (not deleted) them to your account folder.
Basically in doc and settings you have each account as a folder, you can move and delete files from there, but be carefull with what you delete or move!!