It is true that we are all essentially the same due to our common human nature, but other aspects of who we are certainly are impacted, particularly as children, by our cultures. That impact comes primarily in five key elements: language, morality, parenting, world view, and autonomy.
One of the most obvious cultural differences is language. While every child learns his own language, of course, a child's language is more than just a vocabulary and grammar. It is also his primary method of communication, and communication is the heart of cultural expression. Whether a child learns a very primitive, uncomplicated language or a language in which there are twenty-seven words for "work," he learns to communicate effectively within his own culture. He must then learn to adapt whenever his cultural environment changes.
Morality is another aspect of childhood development which is shaped by culture. It is true that most morality is transferred to children by their parents; however, different cultures value different moralities. In the Native American culture, for example, a child is taught that looking an adult directly in the eyes is disrespectful; in many other cultures, however, not making this kind of eye contact is seen as being disrespectful. What a culture values is generally reflected in the morality its children learn.
Parenting styles are different in many cultures, which of course has a dramatic impact on the children. It is easy to understand that Asian and Middle-Eastern cultures, for example, believe that American parenting is too lenient or casual, while Americans can see the parenting styles of these two cultures as quite restrictive. In either case, the children will grow up to reflect the type of cultural parenting they were given.
World view is a bit more difficult to document than some of the other things on this list, but it is world view which demonstrates how a person views the world. A tribal culture's world view, for example, is likely to be much less global than a more advanced and connected culture. Children of a tribal culture will probably be more concerned about the welfare of the tribe than the broader world. This particular component of culture may be due more to economic, geographical, and other things than anything else, but children learn and adopt the world views of their cultures.
Finally, autonomy is a cultural element that determines children's connectedness to family.
According to child development expert Beth Maschinot in her book "The Influence of Culture on Early Child Development," Western morals emphasize self-expression and the standard Western parenting style emphasizes freedom of growth. This leads to parents reinforcing autonomous behaviors in daily circumstances, such as in giving their children choices throughout the day (e.g., "What color crayon would you like to use?" and "Which fish should we choose?")
In contrast, the Asian culture reveres age, wisdom, and experience and promotes family above all else. As a result, Western children are more apt to leave home to pursue their own lives rather than to stay physically connected to their families. Neither is better than the other; they are just different.
In the end, each culture has all of these elements and more; the differences are created because of what each culture choose to emphasize and promote. These things are taught, consciously or subconsciously, to children in every culture. Children are reflections (products) of their cultures.