Difference between Power user and Administrator

What would be the differences between a power user and administrator user?

I assume you mean in a Windows system. Here's the full list from Microsoft:

Basically, Power Users can:

• Run legacy applications, in addition to Windows 2000 or Windows XP Professional certified applications.
• Install programs that do not modify operating system files or install system services.
• Customize systemwide resources including printers, date, time, power options, and other Control Panel resources.
• Create and manage local user accounts and groups.
• Stop and start system services which are not started by default.

Power Users do not have permission to add themselves to the Administrators group. Power Users do not have access to the data of other users on an NTFS volume, unless those users grant them permission.