What is the difference between mva and mw?

For clarification, the correct symbols are 'MV.A' and 'MW' -where a capital 'M' represents 'mega'. A lower case 'm' stands for 'milli' -quite a difference. And the symbols for ampere and volt are an upper case A and an uppercase V.

When an electric current flows through a load, the temperature of the load increases above ambient temperature, and energy is therefore lost to the surroundings through heat transfer. This represents a permanent loss of energy from the circuit. The rate at which this energy is lost is called the true power of the circuit, measured in watts.

At the same time, whenever current flows, a magnetic field is set up around the conductor. As the current increases in value during the first quarter-cycle, this field expands and energy is stored within that field. During the next quarter-cycle, as the current reduces in value, the energy stored in the magnetic field is returned to the circuit. So, while there is movement of energy, there is no net loss of energy from the circuit. The rate at which this energy transfer is taking place is called the reactive power of the circuit, measured in reactive volt amperes. (A similar thing happens in capacitive circuits, although the energy is stored/returned in an electric, rather than in a magnetic, field).

The vector sum of true power and reactive power is called the apparent power of the circuit, measured in volt amperes. That is:

(Apparent Power)2 = (True Power)2+ (Reactive Power)2

(Technically, there is absolutely no reason why true power, reactive power, and apparent power can't all be measured in watts -it is only traditional to use different units!)

It is very easy to measure the apparent power of a circuit, because it is the product of the voltage applied to the load and the current flowing through it -and we could use a voltmeter and an ammeter to determine these values. It is rather more difficult to measure the true power because the voltage and the current must be multiplied by the load's power factor, which is not necessarily known. Nevertheless, it can be measured directly, using a wattmeter.