1. The war would have
turned out different had Britain thrown its full might.
2. The war would have turned out differently had Britain thrown its full might.
At school, I learned that verbs such 'appear, 'seem', 'prove' or 'turn out' are used only with adjective if the verbs indicate the status or characteristics of the subjets(intransitive verb), as you can see in the example 1.
However, I found some professional articles in which adverbs, not adjectives, were used, as you can see in the example 2.
If it is possbile, can it be possilbe to write this way? : She seemed nervously on the stage,The theory proved falsely, and so on. I don't think so. Can anybody help me understand this?