That’s an excellent question, there isn’t really any difference.
1. Adjectives: “Pejorative” is a synonym of “derogatory” so a lot of the time they can be used in very similar ways. However, a slight difference could be that “derogatory” is someone who tends to derogate, (lessen in value of someone) whereas “pejorative” is disparaging or belittling, almost make fun of them in a way that derogative could be seen as having contempt for something. But as I said, there is very little difference as adjectives. “Disparaging” is the same as “pejorative”, arguable more commonly used. I would say that the difference is with disparaging is it also shows a little disappointment. For example, a mother can be disparaging of her son in a way that belittles him but also shows that she expected more.
2. As nouns, however, the difference is a little clearer. “Derogatory” is a trade-line on a credit report that includes negative credit history. “Pejorative” is a disparaging, belittling, or derogatory word or expression, like how it is used as an adjective.
Overall, I wouldn’t worry too much about the difference as they are so similar! I hope this helped and if you have any further questions please feel free to get in touch
https://www.italki.com/maddie.