Both translations miss the initial phrase, "what about you?" The "what" is not repeated in the second sentence but assumed from the context. The Jesus usually asks questions as directly as possible. This question was asked of the Pharisees as a group. They had no doubt about its answers, responding that the "anointed" was David's son.
This is the first time the term "christos" is used in the Bible. The word "Christ," meaning "annointed," is not translated in the KJV, but it is used as a title, is was understood toe refer to the Messiah. The concept of anointing someone goes back to Exo 29:7 where it describes the installation of Aaron, Moses's brother, as a high priest in terms used to describe the crowning of a king.