Difference Between "Wii" and "Nintendo Wii"? None — Same Console

None. They are the exact same console.

• Full branding: Nintendo Wii (logo: "Wii" with two 'i' figures).
• Colloquial shorthand: Wii.
• Model number: RVL-001 (original), RVL-101 (GameCube-port-less revision).

No hardware, software, or regional differences — just naming preference.