During the period from 1820 to 1850, the North and the South definitely diverged from one another. They diverged in tangible ways and they diverged in terms of their attitudes towards one another. This process did not start in 1820 and it did not end in 1850, but it did continue over that time and the two sections of the country grew farther apart and closer to war.
Tangibly speaking, the two sections grew apart in things like their economies and their populations. In 1820, the economy of the South was already heavily centered on cotton, but not to the extent that it would become. For example, Tindall and Shi tell us (in America: A Narrative History Fifth Edition, p. 488) that from 1815 to 1819, cotton made up about 39% of the total of all American exports. From the mid-1830s on, though, they accounted for more than half of the value of all exports. This shows that the South was becoming more and more dedicated to growing cotton for export. In the meantime, the North was becoming more industrialized. It was producing more goods, mainly for domestic consumption. This means that the economies of the two regions were becoming more distinct than they already had been in 1820.
It is also worth noting that the two regions grew apart in terms of transportation links, which are a part of the economy. The building of canals and roads connected areas mainly on an east-west basis. For example, the Erie Canal connected the Great Lakes region (which included the entire Midwest) to New York City in the east. This meant that connections were growing between east and west, but not between North and South.
The two sections also grew apart in terms of population. During these years, immigrants came in relatively large numbers to the North (particularly in the 1840s). Immigrants were not very likely to come to most parts of the South. Immigrants perceived a lack of opportunity in that region because it was so thoroughly dominated by plantations and slavery. This made the two societies even more different. The North became a densely populated multi-ethnic (at least in terms of different groups of white people) society while the South was more homogeneous (in its white population) and less dense.
Perhaps even more important were the ways in which the two sections grew apart in their thinking. As events occurred over these years, the North and the South came to feel that they had separate interests. One major example of this can be seen in the Nullification Crisis of the late 1820s and early 1830s. This was when South Carolina tried to nullify the Tariff of 1828 because it felt the tariff benefitted the North at the expense of the South. South Carolina even threatened to secede. This shows the two regions becoming less connected psychologically. A second example came at the end of this time period, when the Mexican-American War came about in 1846. People in the North felt that this was a war that was being fought to expand slavery while those in the South supported it.
In all of these ways, it is clear that the North and the South were diverging during this time period. This divergence accelerated in the 1850s, leading to the Civil War.
The North and South diverged because of many reasons. Many changes were occurring in the country at this point. The North was industrializing while the South's agricultural heritage drew the two regions apart. The agricultural economy shifted into one based on wages and services. Urbanization also played a huge role because the US had been a land of farmers, but that was the beginning of immigration and movement into cities. The immigration meant the need for more jobs and materials. The South remained predominantly agricultural and this difference is economies and way of life meant differences in opinion and ideologies. This, of course, led to the civil war.