This is not exactly my homework, but then it is a very typical basic question,i am not able to find.What exactly is difference between gain bandwidth and gbp?.

Can I use an opamp having bandwidth of 10000kHz in operating frequency of 1MHz. What should be taken into the account, the gain bandwidth product or the bandwidth,while choosing an opamp for a particular application?

 

I hadn't heard of the term GBP before so I looked it up on Wikipedia. It seems that while BW of an OpAmp is the open-loop 3-dB bandwidth, the GBP refers to the closed-loop feedback assemby of an amplifier. It is the product of the required loop gain and the available 3-dB frequency of the closed loop assembly.
For example, imagine an inverting assembly of an opamp that has GBP of 1MHz. If the forced gain (through the feedback - R2/R1) is 10V/V, then the 3-dB frequency is 1MHz/10=100kHz.
If the forced gain is 1000, then the resulting 3-dB frequency is 1MHz/1000=1kHz.

Acounting the above, when you plan to use an OpAmp in a feedback topology (that is... almost always), you will need to know the GBP, in order to divide it with the desired gain and get the limitations in frequency of your circuit.
However, I have never heard so far a special reference to be made for the GBP, as it can be calculated directly and easily through the open-loop gain of the OpAmp.

 

My understanding is that they are the same number but have a very subtle difference in definition.

"Gain bandwidth product" refers to what Georacer mentioned, that voltage feedback opamps follow a basic rule:

Bandwidth of closed loop op amp = GBP / Gain of closed loop op amp

FYI the gain is the 'noise gain' which is the non-inverting gain, even in an inverting configuration. This gives the inverting configuration lower gain [Rf/R versus 1+Rf/R] for the same bandwidth as the non inverting [GBP / (1 + Rf/R)].
http://www.ecircuitcenter.com/Circuits/op_bandwidth1/op_bandwidth1.htm

So you use GBP in these equations.

"Gain bandwidth" means the open loop bandwidth at which you have a gain greater than 1. However, because the op amp follows the gain bandwidth product rule it gives you the same result:

Gain bandwidth = GBP / 1 = GBP