In the period of 1820-1850, how were the North and South different?
During the time period that you mention, the North and the South were very different in terms of their economies and their cultures. These differences grew more pronounced during the time period that you mention. Later, they would become even worse and would lead to the Civil War.
Perhaps the most obvious difference between the North and the South had to do with their economies. The South’s economy was, of course, built on slavery while the economy of the North was built on free labor. This was not, however, the only difference. In the South, the economy depended on the production of staple crops that would be exported. As the time period that you mention progressed, the South came to depend more and more on cotton. By contrast, the North had a much more diversified economy. Importantly, its economy included manufacturing. This meant that the North had much less interest in foreign trade (which would compete with its manufacturing) than the South did (since the South needed to export). These differences in their economies led to such things as the fight over the Tariff of 1828.
At the same time, the North and the South were developing very different societies. Northern society was a more egalitarian society. This was because the Northern economy was more egalitarian. Northern society also attracted many immigrants because the Northern economy offered them more opportunities. By contrast, the South’s society was dominated by planters who saw themselves as an aristocracy. The South held to romantic ideas of personal honor and chivalry. This is why, for example, the culture of dueling was more developed in the South.
Thus, the North and the South differed in terms of their economies and their societies during the time period that you are asking about.