While the Nintendo Wii U console plays a majority of Wii games, a Wii console does not play Wii U games. To play any Wii U games, the Wii U console is required.
The Wii U is backwards compatible, which means it plays previous generations of games made for the Nintendo Wii. The Wii U console also allows a person to access WiiWare and Virtual Console games that may have been previously purchased on the Wii. Because the Wii U is a new generation of gaming for Nintendo, Wii U games cannot be played on the previous generation Wii console.