There is more than one way to generalize.
The generalization process has simplified the child's world immensely. Instead of having to learn a name for each pattern (20 in our little model world) the categories (inner language, if you will) have reduced the need to learn only four.
One might think that the generalization process was just a straight forward matter of classifying objects on the basis of common bonds.
This may be true except that there are a number of different strategies that children (and adults at times) use, which vary in their effectiveness. Vygotsky described four the first three of which are common among pre-schoolers: Syncretistic, Complexes, Pseudo Cencepts and Full Concepts.