Are North Koreans and South Koreans "same people" or "the same people"? Which is correct: the same or just same, and why?
You would use the definite article there:
North Koreans and South Koreans are the same people.
Same without the article is often used in a telegraphic style (one that omits extra words for the sake of brevity), such as product orders:
"You requested 52 greeting cards: will ship same within 4 days."
In this case it functions as a demonstrative pronoun, whose antecedent is the cards mentioned. Another way to say that is
"You requested 52 greeting cards: we will ship those to you within 4 days."
It fine to use either, but same in that context is a conventional usage.