The Joule is the basic SI unit of energy and is used to measure both heat, work and electrical energy. As a unit or work, it is defined as the work done by a force of one newton acting on an object to move it through a distance of one metre in the direction the force is applied.
The Calorie is an old measurement of heat energy defined by Frenchman Professor Nicolas Clément in 1824. From the Latin Calor meaning heat. It also has its roots in an old theory that caloric was an invisible weightless gas that was responsible for the transfer of heat from hot to cold.
One calorie is the energy required to raise one gram of water through 1°C. This does vary depending on the temperature (and density) of the water but is approximately 4.19 Joules
A confusing variation of this is the food calorie which is also a measurement of energy. However the food calorie (or more accurately the kilogram calorie is the energy required to raise 1kg of water through 1°C, or to put it another way a food calorie is 1000 standard calories or approximately 4.19kJ. A 100 gram portion of a Mars Bar contains 440 kcalories or 440000standard calories which is equivalent to 18,436kJ/kg.
The British Thermal Unit (BTU) is the old imperial (UK) unit of heat energy. It is the energy required to raise 1 pound (lb) of water through 1° Farenheit. It still used today especially in The UK where it is used to define the heating output of domestic boilers and central heating systems.
It will take 2.2 BTUs to raise 1kg water through 1°F and because 1°C = 1.8°F, then it takes 2.2 × 1.8 = 3.96BTUs to raise 1kg water through 1°C which is equal to 1000 calories or 4.19kJ.
or to put it another way 1 BTU = 1.06kJ or 252.5 calories
Often heating or cooling capacity is measured in BTU/hr. So to convert BTU/hr to kW, multiply by 1.06 (kJ/hr) and divide by 3600 (kJ/sec)
e.g. 10 000BTU/hr = 2.94kW
So you could refer to a 3 kW electric kettle as a 10000BTU/hr kettle. (almost)