Yes,there is a small different. Infacts,they are just an ordinary resistor.
A shunt resistor uses in a current meter design to make a current meter able to measure much bigger current than it is rated. For example, a current meter that is able to measure 1 ma in full scale,has internal resistance (moving coil resistance) of 1000 ohms. By parellel a resistor of 0.001 ohm with this current meter. It becomes able to measure up to 1000 ma in full scale. This 0.001 ohm resistor is called "a shunt resistor". Because 999 ma is passed through it when measure a 1 ampere source.
A current sense resistor usually uses in current control device ,like the power supply that has a current limitter control.
In this case,this current sense resistor has a variable resistance (potential meter). It converts the current into voltage drops acrossing the current sense resistor. This small voltage drops is feeded to a simple comparator circuit and futher control to output of power supply.
Conclusion:
DIFFERENCE:
A shunt resistor is used to bypass the unwanted current.
A current sense resistor is used to convert current that being monitor into voltage drops. This voltage drops is futher used to control other device.
NO DIFFERENCE:
They are just a two legs ordinary resistor.