Delete Users and Separate User and Groups
Normally, if you download something (apps, files, anything): it is saved in your User account's Download folder.
When applications arrive, it is usual to copy or install them into the root level /Applications folder. This location is accessible to all users.
If you want applications to be available to only one user, then move them to <user>/Applications. You may need to create this folder inside your user account.
Install the apps you want to use as both users in ~/Public. This works even for users without administrator rights.