The definition is that indeed, immiscible solvents form two separate layers, but not only. Solvents with low miscibility to each other, can also form two separate layers. However, the content of each solvent in each separate layer depends on their logP value that reflects on their solubility to each other.
Thus, when mixing n-butanol and water, the aqueous layer contains n-butanol up to 7.3%. Similarly, when extracting n-butanol with equal volumes of an organic solvent and water, ≈12% of n-butanol is passing into the aqueous phase.