In OS X, as a limited user I used Terminal to su - [admin's name] and tried to move some files that were in the administrator's public drop box directory into /usr/bin. Couldn't do it. Permission denied. The Terminal prompt was clearly in the admin's login shell/environment. Then, I discovered that, from the limited user's login, I could use the menu system to navigate into /usr/bin. I could then move the same files (copies in my directory, not the admin's copies) into /usr/bin as long as I authenticated as admin. Seems backward. How is it that a limited user could get into the /usr/bin directory with administrative authentication, but the admin--at least a user in the admin's shell--could not? 
Terminal access permission denied, but GUI access okay. Why?
permissions;osx
The issue here is that the GUI is not doing what you think it is doing. Neither the terminal nor the GUI can write to /usr/bin (which usually has owner: root:root and permissions: 0755/drwxr-xr-x) as an admin. Only the owner of the directory - root - can do that.However, the GUI has knowledge about what permissions are available and are needed for different operations. It created the concept of admin to refer to someone who can, by entering their own password, become root. So when it prompts you for permission, it actually checks against the admin list and the executes it as root.