If the Mexican-American War had ended differently, with Mexico winning or with the war being a draw, California would likely have remained part of Mexico. This would have had significant implications for the state's history and culture.
For one, California would have continued to be a part of Mexico and not become part of the United States. This would have meant that the state would have a different political system, legal system, and economic system. The impact on immigration to California would have also been different as it would not have been a part of the United States, and thus may not have experienced the same influx of people as it did during and after the Gold Rush of 1849.
The culture of California would also have been different. For example, the dominant language would have been Spanish instead of English. California's art, literature, music, and food would have been influenced by Mexican culture instead of American culture. Additionally, California's social and political issues, such as civil rights, immigration, and border control, would be vastly different.
It is difficult to predict how different California and our lives would be if the Mexican American War had ended differently, but it is clear that the state's history and culture would be vastly different.