Getting to the basics, the energy concept comes first. It corresponds to the amount of work that has to be developed to perform a certain task. For example, the amount of work needed for an electric motor to displace a mechanical load from one place to another is energy. Power is, as you said, the rate at wich energy is delivered, consumed, tranferred. For example, when a generator produces at 5 MW, it means it is producing energy at a rate of 5 MJoules/second. This energy flows through the interconnecting network and is delivered to several loads, i.e., equipment devices that consume different amounts of energy to deliver energy services like lighting, mobility, air conditioning. Each device consumes energy for delivering the energy service it is intended to. A lamp will consume, for example, 80 Joules/second to illuminate a room, which means it consumes energy at a rate of 80 Watts.

Energy management is about how we can provide an energy service at an adequate level (sufficient light, for example) with miminum energy consumption. If we use a compact fluorescent lamp (CFL) instead of an incandescent lamp, the example above could be about a 20Watt CFL instead of an 80Watt incandescent lamp. The energy service (lighting at an adequate level) would be equivalent with a much lower energy consumption. The lamp replacement would have been an energy management measure. If, for example, the CFL is left on when nobody is in the room, switching it off automatically by occupancy detection will save energy by not allowing the energy service to be delivered when it is not necessary. This will also be energy management, although not because we replace the lamp with a more efficient one, but because we managed the use of energy for lighting through automation.

Power management is about the need to limit the rate at wich energy is consumed. It may be because of capacity limitations or because of economic reasons. If, for example, a distribution company is facing the need to increase the capacity of a substation because of some urban expansion that imposes high power demand at certain hours of the day, it may prove to be more interesting to stimulate consumers to shift some energy services to hours (usually at night) when the substation is not so stressed - for example, a special night tariff may be created to encourage people to use washing machines at night instead of during the day.This will alleviate the total power demand (the rate at which energy is demanded) on the substation and allow the distribution company to postpone investment in new transformers. This is power management - modify the profile of energy demand to some purpose. 

I think energy management refers to the control, utilization and planning of energy sources such as electrical power, gas or even petrol, diesel or coal. These are some of the sources of energy. Power management would refer to management of electrical power, generation, distribution and utilisation.

The Energy term is usually used for those researchers who are not electrical engineer but are highly involved in this area. 

KW management is called power management, which generally, all utilities are doing  for better system efficiency, and getting highest return. Energy management is KWH management, which can indirectly implemented, by doing KW management, yet under special circumtances (duration of excess generation,off peak time), consumer is charge special terrife for perticular time, at higher/lower rate for better business, called the energy management.

Energy management is all to do with consumption by the end user, and it is is measured in different units (kW hours). From a management perspective, it is concerned with minimising the cost of electricity supplied and more efficient use of resources.

Power management is measured in kW and is all to do with the physical capability of the electrical supply system to provide the power required to operate a "device" whilst ensuring the system design is fit for purpose and meets the relevant electrical safty regulations (eg, an electric kettle may be rated at 3 kW - this figure is then used to ascertain the current based upon the working voltage, which will ultimately permit the correct system design andf protection settings to be designed and specifiied).

I think Simon is closest to nailing the definitions but you should be aware that the terminology could mean different things to different people depending on their individual area of interest. It can also mean different things depending on where in the system you sit - so a consumer might think differently about energy management than a generator. If you can be more specific about the context of the question, it may help focus the answers you'll receive.

As a starting point, the distinction between power and energy is relatively simple to explain, but for the benefit of those who aren't familiar with it, here's a very brief explanation. Power is an instantaneous measure of work done - the SI unit of power is the Watt (W). Energy is a measure of the power used over time - the SI unit of energy is the Joule (J). However, both of these units are very small and you will typically see power measured in kilowatts (kW) i.e. W / 1000 and often energy measured in kilowatt hours (kWh), 1kWh = 3600kJ. Depending on the type of energy, you may see it measured in MJ or GJ (J x 1,000,000 and J x 1,000,000,000 respectively).

Hope this is helpful.

Energy management is related to the control of the produced power from the available power like in wind farm or solar plant and the techniques of optimisations. the power management is related to control this produced power from plants in whole grid by so called dispatch system.

1) In coloquial English there is no difference.

2) In strict technical language may be: Power = d_Eenergia / d_time

Energy is supplied applying a Power over the time.

For Ex.: You can consume 168 MWh in a Week in several ways. For example, applying 1 MW of Power all te hours of the week or applaying 168 MW in only one hour and 0 (cero) MW all the rest.

So Power Management, refers to the managament of the Capacity of the installation. For example you manages the start up of motos in an industry to avoid simultaneity and so avoid the needing of increase the Power Capacity of your system.

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So I think that the correct interpretation (1 or 2 ) depends on the context where you are reading the terms.

Getting to the basics, the energy concept comes first. It corresponds to the amount of work that has to be developed to perform a certain task. For example, the amount of work needed for an electric motor to displace a mechanical load from one place to another is energy. Power is, as you said, the rate at wich energy is delivered, consumed, tranferred. For example, when a generator produces at 5 MW, it means it is producing energy at a rate of 5 MJoules/second. This energy flows through the interconnecting network and is delivered to several loads, i.e., equipment devices that consume different amounts of energy to deliver energy services like lighting, mobility, air conditioning. Each device consumes energy for delivering the energy service it is intended to. A lamp will consume, for example, 80 Joules/second to illuminate a room, which means it consumes energy at a rate of 80 Watts.

Energy management is about how we can provide an energy service at an adequate level (sufficient light, for example) with miminum energy consumption. If we use a compact fluorescent lamp (CFL) instead of an incandescent lamp, the example above could be about a 20Watt CFL instead of an 80Watt incandescent lamp. The energy service (lighting at an adequate level) would be equivalent with a much lower energy consumption. The lamp replacement would have been an energy management measure. If, for example, the CFL is left on when nobody is in the room, switching it off automatically by occupancy detection will save energy by not allowing the energy service to be delivered when it is not necessary. This will also be energy management, although not because we replace the lamp with a more efficient one, but because we managed the use of energy for lighting through automation.

Power management is about the need to limit the rate at wich energy is consumed. It may be because of capacity limitations or because of economic reasons. If, for example, a distribution company is facing the need to increase the capacity of a substation because of some urban expansion that imposes high power demand at certain hours of the day, it may prove to be more interesting to stimulate consumers to shift some energy services to hours (usually at night) when the substation is not so stressed - for example, a special night tariff may be created to encourage people to use washing machines at night instead of during the day.This will alleviate the total power demand (the rate at which energy is demanded) on the substation and allow the distribution company to postpone investment in new transformers. This is power management - modify the profile of energy demand to some purpose. 

In the strict sense, energy management is often related to energy for plant manufacturing use, for example coking coal, water, electricity, wind and gas. Yet power management involves only electricity consumption.