In the 1950s, the big money shows were generally referred to as quiz shows. Unfortunately for the genre, the quiz show scandals occurred, which nearly destroyed the entire genre. The term "game show" is more common in the US today, and one reason is that producers did not want to connect new shows to the rigged shows of the 1950s. Further, shows using quiz questions basically disappeared until the premiere of Jeopardy! in 1964, which, owing to the scandals, provided the contestants with all the answers but made them come up with the questions.

Whether "game show" or "quiz show" is used depends on the country. However, quiz shows carry the connotation of answering questions, while there are many game shows that do not involve trivia at all (for example, The Dating Game and Match Game).

no they do not. The answers are not allowed to be provided to game show contestants. They would break federal laws inacted in 1960 after a scandal.

from wikipedia

The American quiz show scandals of the 1950s were a series of revelations that contestants of several popular television quiz shows were secretly given assistance by the show's producers to arrange the outcome of a supposedly fair competition. The quiz show scandals were driven by a variety of reasons. Some of those reasons included the drive for financial gain, money, the willingness of contestants to "play along" with the assistance, and the lack of current regulations prohibiting the rigging of game shows.

The United States Congress passed the 1960 amendments of the Communications Act of 1934, preventing anyone from fixing quiz shows