Can you tell the difference between norovirus and rotavirus based on symptoms alone?

There are distinct difference in presentation: Rotavirus infection begins with acute onset of fever and vomiting followed 24-48 hours later by watery diarrhea whereas norovirus infection presents as abrupt onset of vomiting accompanied by diarrhea, abdominal cramp, and nausea. The symptoms of rotavirus infection are not specific enough to distinguish from other viral gastroenteritis.