What exactly are the Domain Security Policy and Domain Controller Security Policy shortcuts I find in Administrative Tools on domain controllers (DCs), and how do they relate to Active Directory (AD) Group Policy Objects (GPOs)? Do the settings in these policies take precedence over my GPO settings?

These shortcuts take you directly to the Security Settings section of the two GPOs that come with AD. When you open Domain Security Policy, you're actually looking at the Computer Configuration\Windows Settings\Security Settings section of the Default Domain Policy GPO, which is linked to the root of your domain. The Domain Controller Security Policy shortcut takes you directly to the same section of the Default Domain Controllers Policy GPO, which is linked to the Domain Controllers organizational unit (OU). Thus, you don't need to worry about precedence--the shortcuts are taking you to the same collection of settings as in the GPOs. However, I recommend deleting these two shortcuts because using them can hide some important details that you typically see when using the Microsoft Management Console (MMC) Active Directory Users and Computers snap-in or the Group Policy Management Console (GPMC). For instance, the shortcuts don't show other GPOs that might be linked to the domain or OU.