If income is altered in response to the price change such that a new budget line is drawn passing through the old consumption bundle but with the slope determined by the new prices and the consumer's optimal choice is on this budget line, the resulting change in consumption is called the Slutsky substitution effect.
The popular textbook by Varian[1] describes the Slutsky variant as the primary one, but also gives a good explanation of the distinction.
The same concepts also apply if the price of one good goes up instead of down, with the substitution effect reflecting the change in relative prices and the income effect reflecting the fact the income has been soaked up into additional spending on the retained units of the now-pricier good.
The overall effect of the price change is that the consumer now chooses the consumption bundle at point C. But the move from A to C can be decomposed into two parts.
The substitution effect is the change that would occur if the consumer were required to remain on the original indifference curve; this is the move from A to B.
The income effect is the simultaneous move from B to C that occurs because the lower price of one good in fact allows movement to a higher indifference curve.