As in the title, is there any difference between the following sentences?
- You'd better put your results to another place.
- You would better put your results to another place.
And, when do I use any of them?
You'd has two meanings, which are you had and you would.1 We use you had with better and you would with rather. You had is usually used for suggestion.
Example: You'd better (you had better) avoid the stalls on the street.
So you'd means you had in your first sentence. Your second sentence is grammatically wrong.
1According to The Cambridge Advanced Learner's Dictionary, Third Edition.
the "had" verb should be followed by a past partciple verb.
You had gone wild. (It happened.) You would go wild. (A possibility or suggestion)
Since "put" has the same forms in all tenses, then it's okay to use any.
You had better put your results in another place. (It happened.)
You would better put your results in another place. (A possibility or suggestion.)