Why are USA under 18 year olds sentenced differently for the same crime(compared to adults)?

They are legally children.  A child, in law, means that they lack the capability to make proper decisions, which is why (among other things), the parents can be held responsible for what a child does, even if only in civil law.

It takes a court judgement to declare that an under-age individual can be judged as an adult and can be assumed to have had the mental capacity to decide for themselves.  Many teens are capable of making adult decisions about some things and not others.  Children, for the most part, are not seen to have that ability.  Full adults are presumed to have that ability whether or not they do, and an adult can be found to lack such a capability due to some mental/cognitive disorder, but it is up to the adult to prove that incapacity (or that adult's representatives, really).

The basic idea is that children are like household animals ("pets").  Whatever they do is because of faulty supervision.  The prosecution has to prove that they should have, and could have, and thus likely did, know better.  Otherwise, they are treated as if this is time to teach that lesson so they will know better the next time.  The idea is to stop future criminal behavior, supposedly.  Clearly, the parents have failed, so now it is up to the court to teach the lesson.

Depends on the crime.   A minor can indeed be trialed and sentenced as an adult for serious crimes.

For lesser crimes, the aim is to rehabilitate the minor so they don't become criminals as adults.

i didn't realize they were sentenced "differently."   In my state, a thirteen-year old was charged with intentional first-degree murder for killing her grandmother.   She was sentenced with life in prison.

not always.  the DA is allowed to petition the court to have a juvenile tried as an adult.  This is usually reserved for repeat, violent offenders.

It depends on the crime.   It depends on the location.   It depends on the judge.   

There can be many variables.  

Generally true, because they have different laws applicable to them [minors]. However, for certain crimes, the minors are charged as adults.  

They are children so not considered so guilty as knowing what they do. Anyway they will often be tried as adults so they can be given the chair. George Stinney was electrocuted in South Carolina at the age of 14, after the bodies of two children were found close to his home.

Because they are juveniles.  They are often tried as adults though.

The courts think they can be rehabilitated.