There are 3 modes for Dwarf Fortress. Fortress mode is the colony builder/strategy type mode. Adventurer is the rougelike/rpg type mode. There is also Legends which allows you to look at the history/data of the world.
For the most part it is very similar to C:DDA, it may be more complex, although I do not have enough experience with C:DDA to truly compare the two.
In Adventurer mode (also called “Adventure mode” or simply “Adventure”) you create a single adventurer, be they dwarf, human, elf, goblin, or one of the varieties of animal people, who start out somewhere in one of your generated worlds. You can learn about what ails the world, and go on quests to end those troubles (or get brutally murdered trying), and you can venture into the wilderness to find caves, shrines, lairs, abandoned towers, and other towns and settlements. You can even visit your previously abandoned/retired fortresses and take all the precious items you yourself once created. Unlike fortress mode, Adventurer mode is a sort of advanced open world RPG version of Rogue or Nethack taking place in the same procedurally-generated worlds used for fortress mode. Whereas in fortress mode, you are in charge of a large group of people in real-time, restricted to a small parcel of land, in adventurer mode you control a single character in a turn-based manner, roaming the entire world freely.