Technically, you are probably right as malato can be used for either ill or sick. The difference comes in the English translation, in that in the UK at least we would only really use sick to mean vomiting or mildly ill, not seriously or gravely unwell. I think this distinction may be less apparent in American English? The only use of the sentence "They were seriously sick" here in England might be if there were to be an outbreak of norovirus which causes profuse vomiting. Even then it would be a bit colloquial.