What is the difference between sakhṭ (displeasure) and ghaḍab (anger)?

It appears from the words of linguists that ghadab (anger) and sakht (wrath/displeasure) are synonymous, as they explain one by the other. Al-Tha'alibi mentioned that sakht is the first stage of ghadab. However, the author of Al-Furooq Al-Lughawiyyah (Linguistic Differences) mentioned a distinction between them: ghadab can be from the small towards the great, and from the great towards the small, whereas sakht is only from the great towards the small.