The difference between incinerator and boiler

is that "incinerator" is a furnace that burns refuse and "boiler" is a person who boils something.

incinerator

A person who boils something.
A steam boiler.
An apparatus for heating circulating water or other heat transferring liquid.
A device consisting of a heat source and a tank for storing hot water, typically for space heating, domestic hot water etc., disregarding the source of heat.
A kitchen vessel for steaming, boiling or heating food.
A sunken reef, especially a coral reef, on which the sea breaks heavily.
(Britain, informal) A tough old chicken only suitable for cooking by boiling.