Do resistors of same color code but different size have the same resistivity?
resistor of same color code but different size have the same resistivity?

No, they have the same resistance.  Resistivity is a bulk property of material.  Since the geometry of each resistor is different, it is quite likely that the resistivity of the material the resistors are made of differ between the resistors.

The resistance, however, is the same (within tolerance, looks like 5%) between each of the resistors.  It's a little hard to tell, but the color bands seem to be BRN,BLK,BLK.  If so, then each resistor is 10 &Omega; &plusmn;5%.

The two main differences between the large and small resistors are:

Power capability.  Large resistors can dissipate more power before getting too hot.

Voltage capability.  Larger gap between the leads usually results in higher voltage handling.  For such relatively low values, the maximum voltage can only occur in short spikes, else the resistor would get too hot.  This metric is more relevant for high-Ohm resistors where the voltage is not limited by power dissipation.