Is the UAC level in Windows per individual user?

The UAC level is a machine wide setting. So it cannot be set per-user.

It sounds as if you want to make it so that elevation occurs silently for admin users but standard users can still enter a password to be elevated.

If your edition of Windows supports Group Policy, you can do this. First, use the control panel GUI to restore the "Always Notify" setting.

Using gpedit.msc, go to Local Computer Policy: Computer Configuration: Windows Settings: Security Settings: Local Policies: Security Options.

Set "User Account Control: Behavior of the elevation prompt for administrators in Admin Approval Mode" to "Elevate without prompting".

Reboot.

It is probably possible to do the same thing via the registry on Windows editions that don't support group policy, but I don't know how to do this.

The setting is written in the HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Policies\System path inside the registry. So it is an system wide setting.

I belive, that in the Professional+ version of Windows you can define the setting using gpedit.msc, which should allow different settings per user.