Injecting a little personal experience, the last time I applied for a Chinese Visa, I applied for a Q, the Consulate of jurisdiction on their own issued me an L visa (with a slightly longer authorized duration of stay than the standard) on their own.
Sometimes you can apply for 1 type a visa and instead of denying the application, they'll just issue the type visa they think you're qualified for.
This would be in the L category.