So, here the difference is between vomiting as a reaction to poisoning and vomiting as a disease category (chardi is used in the latter sense in the Śārṅgadharasaṃhitā). My impression (this was a very quick look) is that vānti and chardi otherwise are interchangeable.
Re kāsapittātisāra: it should divide into kāsa (cough - there are different kinds of kāsa, it's a category of disease) and pittātisāra, flux caused by pitta (one of three humoral substances, or doṣas).
Then, it should be pittakāmalā, kāmalā (something like jaundice) caused by pitta.