The participation of individuals in such ceremonies was called 'festival,' and a prayer for good luck charm such as Jichinsai, Doll's Festival, Setsubun (the traditional end of winter) and so on is equivalent to it even now.
また、個人がそういった儀式に参加することも「まつり」であり、現在でも地鎮祭、ひな祭りや節分などの招福祈願がそれにあたる。