These are very close, and there is some overlap, but I tend to use "disparaging remark" when I mean that something was said to someone to belittle them or bring reproach upon them, or cast doubt about their abilities, and derogatory when I mean a remark that was made to damage someone's reputation or someone's opinion of that person. examples: The director's disparaging remark about her acting ability left Stella wondering if she should abandon the idea of a career on the stage. The director's derogatory remark about Stella's behavior at the cast party made John wonder if he wanted to continue to try to develop a relationship with her.
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