Negative can just mean "not" so "not ugly" is a negative phrase, but it's not pejorative
But "pejorative" means specifically expressing disapproval. So a word like "stupid" is pejorative (or can be used in a pejorative sense), but the sentence "He is stupid" doesn't use any negation.
However "pejorative" is a much rarer word than negative and the senses of negative can stretch to mean "bad". Not everyone has the rare word "pejorative" in their vocabulary so the more general term "negative" can be used instead.
Moreover, calling something "pejorative" implies intent to insult or criticise. Consider the word "crusader". This word is used by some people as a pejorative, but by others as a complimentary word. It depends on your viewpoint about the crusades.
Pejorative is also a fairly new word. It was even rarer prior to 1950, and is still a rather technical word. Simpler words is "slur" or "insult".
Is "crusader" a slur?