There was indeed a Toyota Cavalier, and yes, it was also a Chevy. Through a partnership with GM, it was a way GM could sell cars overseas without having to break the export rules. The car was not a hit overseas because of its small size and American flavor. We know that the Cavalier itself felt very cheaply made, and that also was the case with this model. All that was done to the car were a few badge modifications and different taillights.
Meanwhile, on the other side of the ocean, Toyota was selling the Corolla as the Chevy Prism. Needless to say, the partnership wasn’t very fruitful for Toyota. GM on the other hand got to market a vastly superior compact car that was reliable and had Corolla underpinnings.