Released a couple of years ago, Tetratris serves as the prequel to Tetratris True. I recommend downloading and playing the sequel instead; however, I make the original available as well for anyone with interest.
Tetratris features multiple unique game modes, including Time Attack mode, Rubik's Spin mode, Twintris mode and, of course, Tetratris (4-way) mode. For more details on these modes (which remain unchanged in the sequel), you can check out the Tetratris True page.
Tetratris also has a high score board, custom background selection and customizeable controls. You can also change the colors of the pieces themselves to better match your custom background if you desire.