Both the words mean ‘end or ending of life'.
‘Demise' is mostly used in formal contexts to refer to the death of someone or something very important or well known.
‘Death' is a much more general term and unlike ‘demise', it can be used with things and animals.
The sudden demise of the Prime Minister created a political vacuum.
The word can also be used to indicate the failure of an enterprise.
Example- The demise of the well-known company made many investors worried.
Example- Niki became very upset when she heard about the death of her puppy.