In which ways was the South restored after the Civil War and in which ways was it reconstructed?
When we speak of Reconstruction historically, the period from 1865 - 1877, it is generally regarded as a dismal failure. Politically, the Union was restored, as the 10% Plan allowed the states to be readmitted into the Union. Constitutionally, the 13, 14, and 15 amendments were added abolishing slavery and giving free blacks citizenship and some voting rights.
Socially, the southern states responded with the Black Codes, which essentially made blacks into slaves again without calling them that. The KKK also emerged at that time as a social police force.
The Freedman's Bureau attempted to bring basic literacy to former slaves, but the funding was cut after only seven years, and the vast majority of former slaves were still uneducated.
Thaddeus Stevens called for "40 Acres and a mule" for every freed slave, but that was not adopted, and most "free" blacks ended up as sharecroppers or tenant farmers, without their own land.
Physically, the South was never fully reconstructed. The industry was gone, and most of the railroads along with it. Some economists suggest the South did not recover economically until the 1980's.
I assume that when you say "reconstructed" you mean "changed" and when you say "restored" you mean "put back to how it was before the war.
I suppose that you could say that the South was reconstructed in terms of slavery and of the legal rights that black people had. That, at least, had to change. Slavery was no longer legal and blacks had, officially, legal rights.
The South was restored to how it had been, though, in terms of its economy and in terms of what rights blacks really had. The economy was still based on agriculture where slack workers worked for large white land owners. Blacks still had very few real rights. So in that way, nothing changed.
After the Civil War the South was left in terrible shape. The lands were burned and there was not much money for reconstruction. Many of the elements entailed figuring out what to do with the freed slaves. Many were displaced and forced to wander hoping to find food, a place to lay their heads, and work.
The education of blacks became a new focus because so many were ill equipped to obtain employment. Booker T. Washington recognized this and developed a school to train men and women in trades as domestic workers and brick makers. Many black people also exited the south and moved north and west.
Rebuilding a political foundation was also necessary in order to prevent further domination from the North. Rebuilding transportation lines such as the railroad was necessary in order to reinstate the ability for trade. There was a large focus in this area.