For Kierkegaard, anxiety/dread/angst is “freedom’s actuality as the possibility of possibility.” Kierkegaard uses the example of a man standing on the edge of a tall building or cliff. When the man looks over the edge, he experiences an aversion to the possibility of falling, but at the same time, the man feels a terrifying impulse to throw himself intentionally off the edge. That experience is anxiety or dread because of our complete freedom to choose to either throw oneself off or to stay put. The mere fact that one has the possibility and freedom to do something, even the most terrifying of possibilities, triggers immense feelings of dread. Kierkegaard called this our “dizziness of freedom.”
Nietzsche later picked it up, himself using Angst as that’s basically the same word as Danish angst (shocking, I know). Danish also has frygt, German Furcht, English fright, which is immediate and not apprehensive. Reactive, not agentive. Fright is something that happens to you, dread is something you do. At least in theory people don’t always make a clear distinction, they’re blending into each other.
Do note how angst is translated as anxiety or dread, here, which is correct. In psychology English uses anxiety where German uses Angst, both existentialists were talking about psychology, which leaves us with the question on why English philosophers felt the need to import the Danish, or German, or whatever, word, when they had two perfectly fine words of their own.