Here is a WIKI definition for heater: http://en.wikipedia.org/wiki/Heater and here is a WIKI definition for furnace: http://en.wikipedia.org/wiki/Furnace
Generally speaking, there are many different types of heaters. E. g. an electric heater (1-2 kW) for the bathroom in the spring or autumn when the heating system in the house is not running. Pocket heaters to warm your hands in the wintertime either battery or gas powered. The heater in the car etc. A heater can be portable.
A furnace is a stationary device - not necessarily - but also used for heating purposes e. g. an incinerator in a morgue. Furnaces are also used for garbage disposal; in modern designs, the resulting heat is used for power generation and heating purposes. Oil or gas furnaces are used in homes solely for heating purposes and hot water availability.