Remember that DF is a world simulation: DF generates a world, creates landscape, cultures, civilizations, cities, etc. It keeps track of every character, significant monster, and legendary artifact. It tracts when they’re born, where they live, their children, whom they kill or who kills them, if they create artifacts, become rulers or get ousted from power, migrate to another city/fort, etc.
It also simulates the civilizations: civs found new cities and forts, go to war against each other, sometimes destroy each other, sometimes trade peacefully.
In fortress mode you join a dwarf civ, then pick a location where your new fort is made. If you are attacked by a Forgotten Beast, it’s not randomly created for that attack. It was born when the world was founded, and has survived hundreds or thousands of simulated years before coming to your fortress.
In Adventure mode, you play in the simulated world like a normal rogue-like. You create one character and head out to adventure in the simulated world. Hypothetically, you can travel to every civilization in the world. Explore ruins of fallen civilizations. Etc, etc, etc.
Legend viewer isn’t a game mode per se: it lets you look at current state of the world, review life history of every character who ever lived, read about legendary Forgotten Beasts, where the beasts went, who they killed, or who killed the beast, see when cities were founded and destroyed, read the names and histories of those who were killed when the city fell or what city they fled to, etc, etc, etc.
I really liked Adventure and Legend Viewer and look forward to them returning. Both modes let you explore DF’s insane level of detail in different ways than running a colony.