Gain BandWidth VS Unity Gain Bandwidth??

There are 2 different parameters

Gain BandWidth Product and Unity Gain Bnadwidth.

My Question:

What's the definition of the two parameters?

What's the differences between the two parameters?

In general,Which is bigger?

In general,When we choose a element such as OP,which one we should take it into consideration?Which one would be ignored compare to the other one?

I post the same topic in another BBS,someone said the two are same,But why must we define the two different parameters even they are same.

ThankS

The gain bandwidth product (GBW) for an amplifier is the product of the open loop gain (constant for a given amplifier) and its 3 dB bandwidth.

This quantity is commonly specified for operational amplifiers, and allows circuit designers to determine the maximum gain that can be extracted from the device for a given frequency (or bandwidth) and vice versa.

When adding LC circuits to the input and output of an amplifier the gain raises and the bandwidth decreases, but the product remains constant.

The gain-bandwidth product may be understood from a conservation-of-power viewpoint. The difference between the output signal power and the input signal power can never be greater than the DC power supplied to the amplifier through its bias circuitry. Stated mathematically, if Pout is the total output signal power from the amplifier, Pin is the total signal power input to the amplifier, and PDC is the total DC power supplied to the amplifier, then

Pout - Pin ≤ PDC

Examples
If the GBWP of an op-amp is 1 MHz, it means that the gain of the device falls to unity at 1 MHz. Hence, when the device is wired for unity gain, it will work up to 1 MHz (GBW product = gain x bandwidth, therefore if BW = 1 MHz, gain = 1) without excessively distorting the signal. The same device when wired for a gain of 10 will work only up to 100 kHz, in accordance with the GBW product formula. Further, if the maximum frequency of operation is 1 Hz, then the maximum gain that can be extracted from the device is 1 x 106.

The product of closed-loop gain GCL and bandwidth fc is constant!

Gain x Bandwidth = GCL x fc = GBP (Gain Bandwidth Product)

What does this mean? If you want to increase the gain GCL, the bandwidth fc will drop to maintain a constant GBP. Alternatively, if you need a higher bandwidth, then lower the gain. If you need both higher gain and bandwidth, pick an op amp with a higher GBP on its data sheet. (GBP may be also called the Unity-Gain Frequency.)

Added after 3 minutes:

Measure of the gain-frequency product of an amplifier; unity gain bandwidth is the frequency at which the open-loop gain becomes unity, based on 6 decibels per octave crossing.

They are the same figure number.
Take the gain at a defined feedback loop and multiply by the bandwidth (from DC to -3dB cutoff frequency) this is the gain bandwidth product that should be constant.
If your gain is 1 (no gain) and the bandwidth is 100kHz, when the gain is 10, the bandwidth will be 10kHz to keep the product constant. With gain = 100, bandwidth is 1kHz and so on.

In Brief,

The "Gain Bandwidth Frequency" (GBW) is the product of the open loop DC gain and the -3dB cut-off frequency.

The "Unity Gain Bandwidth" (UGB) is the frequency where the open loop gain is unity.

These two frequencies are the same if the system (e.g. OPAMP) is a one pole system, that means the second non-dominant pole is at very high frequency.
If second poles and/or zero'sare close or lower than UGB, the two parameters are not equal.
The two parameters (UGB and GBW) are related to the maximum frequency you could your system in closed loop configuration. That is, if UGB ad GBW is 1 MHz, your system cannot work at higher frequency tham 1 MHz since the gain in the loop is lower than 0 dB and all advantages ot the feedback are lost.

Can someone tell what exactly is the physical interpretations of Gain bandwidth and unity gain bandwidth ?