In general, energy is power * time. So energy and power are not the same thing.

Specific power is power per unit mass, and specific energy is energy content per unit mass. So again the quantities won't match, except in the case of time = 1.

In steady state, typically power will be a constant, and specific power would also be constant (unless you factor in the weight of fuel being lost steadily in a hypothetical fuel tank), while the energy consumed would be increasing linearly.

Let me give you a simple example deepak. They can be compared with a "bottle" and a "cup". The bottle has higher capacity but will require more time to be filled. Similarly, the content can not be depleted immediately. to the contrary, a cup has less capacity but can be filled and depleted very fast. In other words, the specific power of the cup is higher than a bottle. However, the specific energy of the cup is lower.

 thank you 

http://batteryuniversity.com/learn/article/battery_definitions

helpful link

Can I consider the specific power as a ''rate of depleted''?@Farshid Naseri