It is difficult to describe the entire non-slave holding majority in the South because this was not a uniform group of people. Some were artisans in cities. Others were poor subsistence farmers. They did not all have the same lives or the same relations with planters and slaves.
We can say, however, that the majority of the whites who did not own slaves were either yeoman farmers or were poor and landless. Yeoman farmers were people who typically owned their own land and were more or less self-sufficient. They would mainly grow things for their own use, but they might also grow a little bit of cotton to sell to get a little cash. By contrast, the poorer, landless whites were often tenant farmers. They would cultivate land for a landowner and were typically in debt to that person.
Not surprisingly, these two groups related differently to other groups around them. The yeomen were of much higher status. They could deal with the plantation owners on something of an equal basis. Plantation owners often bought food for their slaves from the yeomen. The yeomen might pay the plantation owners to process and sell the cotton that the yeomen sold. They had something of an equal relationship with the plantation owners. They might sometimes hire slave labor as well. They did not interact with the slaves as equals in any way.
By contrast, the poor whites were in a much more subservient position with respect to the plantation owners. They were often in debt to them. Sometimes they worked for these landowners. This put them, at times, on nearly the same level as slaves. They often had to work along with slaves at similar jobs. They sometimes interacted with the slaves socially. However, these people still tended to support the plantation owners and the slave system. Historians say that they did so because the slave system allowed them to feel superior to blacks. Without slavery, they would not have had anyone to be superior to.