Definitions from Oxford English Dictionary:
Anxiety - a feeling of worry, nervousness, or unease, typically about an imminent event or something with an uncertain outcome.
Angst - a feeling of deep anxiety or dread, typically an unfocused one about the human condition or the state of the world in general.
- If the source of your unease is something specific (such as financial worries or fear of death), you're experiencing anxiety.
- If the source of your unease isn't focused on something specific (such as "everything sucks and we're all doomed"), you're experiencing angst.
Angst is derived from German. Danish philosopher Søren Kierkegaard coined the term in his book The Concept of Anxiety:
In Existentialist philosophy the term angst carries a specific
conceptual meaning. The use of the term was first attributed to Danish
philosopher Søren Kierkegaard (1813–1855). In The Concept of Anxiety
(also known as The Concept of Dread, depending on the translation),
Kierkegaard used the word Angest (in common Danish, angst, meaning
"dread" or "anxiety") to describe a profound and deep-seated
condition. Where animals are guided solely by instinct, said
Kierkegaard, human beings enjoy a freedom of choice that we find both
appealing and terrifying. It is the anxiety of understanding of
being free when considering undefined possibilities of one's life and
one's power of choice over them. Kierkegaard's concept of angst
reappeared in the works of existentialist philosophers who followed,
such as Friedrich Nietzsche, Jean-Paul Sartre and Martin Heidegger,
each of whom developed the idea further in individual ways. While
Kierkegaard's angst referred mainly to ambiguous feelings about moral
freedom within a religious personal belief system, later
existentialists discussed conflicts of personal principles, cultural
norms, and existential despair.