The Old Testament is the name given to the Torah by Melito of Cardis in the 2nd century BCE. It is comprised of the 24 books of the Hebrew bible or Tanakh. It is a collection of Hebrew writings, and the New Testament is written in Koine Greek.
While the New Testament is definitely a lighter, kinder book, the Jewish people do not see it as a companion to the Torah. A Jew would not refer to the Torah as the Old Testament–however, it is nice when flexible, kind Jews do not judge another Jew who does. This same theory can also be used when talking about the use of the letters BC (“Before Christ”) and AC (“After Christ”) as a way to mark western time. A Jew will use BCE (“Before the Common Era”) and ACE (“After the Common Era”) when referring to Western time in order not have to create another way of counting time (besides obviously when using the Hebrew calendar which starts at a year zero that was calculated by adding up the ages of all the descendants of Adam and Eve described in the Bible).