It could of course be a related illness, caught by both family members and fatal for them, while others in the family survived the same illness. On the other hand the deaths may not have been illness related, for example I have a father and son who died in the same quarter of 1856, but the son died on April 1st from TB at the age of 50 and his 80 year old father on June 20th 1856 from "apoplexy" - stroke, maybe. Not the same day, as your example, clearly, which could indicate a related illness, such as an epidemic or local outbreak of some disease.
The death certificates could well be the only way you will find out, if there is no newspaper report on this tragedy.