Hello, this is Emily.
Do you have any context where you saw the administrator account vs. local administrator account?
Administrator account is more of a general concept. Under administrator account type, there can be domain administrator (an admin user that works for te entire business network) and local administrator (admin right is only in the scope of the device itself).
As for Local vs. Standard account, i think you meant local account vs. standard account?
Local admin has full control but only over the local machine, meaning it can manage settings, install software, and manage other accounts on that particular computer.
A standard account does not have as broad permissions as an administrator account. It can use software and make some settings changes, but it cannot install new software or change security settings.