The terms we use to describe them are descriptive and prescriptive. You can probably figure out what they mean. Descriptive dictionaries describe the language. They include words that are commonly used even if they are nonstandard. They will often include nonstandard spellings.
Prescriptive dictionaries tend to be more concerned about correct or standard English.
They prescribe the proper usage and spelling of words. That school dictionary in which I found ain't was a descriptive dictionary. The truth of the matter is that today virtually all English language dictionaries are descriptive. The editors will usually say that they are simply recording the language and how its words are used and spelled. True, there may be some guidance.