What is the difference between Hicksian and Slutsky theories in the demand curve?

Demand curve proposed by John Hicks expresses a demand for consumption bundles when the utility is fixed for the consumer as the expenditure is reduced. Hicks compensated demand curve separates the price effect into substitution and income effects through the compensating income variation caused by the change in the relative price of a good, keeping the real income constant. The demand curve isolates the substitution effect. It illustrates that the consumption after the price change is compensated in such a way that it allows the consumer to have the same utility as before.

The demand curve proposed by Eugen Slutsky expresses the changes in demand for consumption bundles due to a price change while the utility is fixed. It states that the change in the demand includes substitution and income effects and they together equal the total change in demand. Slutsky compensated demand curve explains the price effect by taking the real income of the consumer as constant. As the price of good X falls, the income of the consumer rises but it is adjusted in such a way that the amount of good X consumed is same as before, so his real income remains constant.