The story actually has two or three settings, depending on how you view them. In its framework, the action is set in the future, presumably in the year 2055. Time travel is possible, but only by following strict requirements. The business called Time Safari, Inc. takes people back in time to shoot and kill exotic, now-extinct animals. The story begins and ends in this office.
The main plot involves a hunting party that uses the time machine to go back to prehistoric days. Their goal is to kill a Tyrannosaurus rex that would otherwise be killed by a falling tree. This setting is obviously vastly different, almost primeval. It’s a tangled green jungle, outfitted with a Path that the hunters must stay on in order to not disturb or injure anything. The dinosaur appears and is killed, the tree falls, and the hunters return to their own time.
But is it their own time? Immediately they notice changes because one of the party members had stepped off the Path. They return to the Time Safari, Inc. office, but things are now slightly different – enough, that it could be considered a third setting. This leads to the point of the story: time travel has the ability and danger of changing the future.