My understanding is that Adventure Mode shares a number of world features with Fortress Mode (item properties, monsters, stats on individual dwarves), but the core gameplay is extremely different. Questions that deal with Adventure Mode should have the dwarf-fortress-adventure tag.
Now, in my experience, when people simply say "Dwarf Fortress", with no further qualifiers, they tend to be talking about Fortress Mode. I don't have numbers to back it up, but I get the feeling that Fortress Mode is much more popular than adventure mode. Because of this, I would advocate only the dwarf-fortress tag be used for Fortress Mode questions, and both tags be used for Adventure Mode. I don't feel like a third tag adds much value.