Is Vacation a Sequel: Short Answer
Yes, Vacation (2015) is a sequel in the sense that it continues the premise of the original National Lampoon's Vacation (1983), but it is a soft reboot rather than a direct narrative follow-up. The new film does not explicitly reference the events or fate of the original family and instead presents a contemporary take on the misadventures of a father and son on the road.
From a production and creative standpoint, it is the fourth theatrical entry in the Vacation franchise when including Christmas Vacation and European Vacation, and it carries the same core concept forward with a largely new cast and modern setting. The next sections break down the franchise structure, cast changes, and how the story positions itself relative to the original.