The distinctions are exactly the same right out of the box, but can be muddied by an Administrator as the level of available control is much more granular.
When a computer joins a Windows Server domain:
- The "Domain Users" group is added to the local "Users" group - meaning all users get the same rights as a local user.
- The "Domain Admins" group is added to the local "Administrators" group - meaning all domain admins become local admins of your machine.
There are a few ways that things can get more complex though:
Group Policy can be used to delegate additional permissions. Group Policy Preferences can be used to add, remove, replace or otherwise tamper with the membership of any local group (you can see your local groups by going to
lusrmgr.msc and look in the "Groups" container)
Group Policy can also be used to allow certain users the rights to do things that they would not normally be able to do as a limited user such as logon as a service, Remote Desktop machines, change the system time without UAC elevation - see This Technet link for a really long list of rights that can be delegated (won't post in answer as its already really long)
Some Active Directory groups have special permissions as well. An example of this is the "Account Operators" group. Membership of this group allows a user to reset the password of other users, allows deletion/removal of a machine from the domain and a whole other list of functions - but does not allow changes that would demote/promote a domain controller, create a new domain or otherwise mess with the AD Schema. This Technet Article explains the default groups and their rights on a standard out-of-the-box domain.
There are other methods that can be used for modifying rights (powershell startup scripts to change registry rights, auto-mapping of printers, auto-install of software etc) - but to go into all of thes epossibilities would make this answer endless. If you can provide a more specific example fo the type of security and rights you are curious about or give us a scenario-based question, we can give a more targeted answer.