Anguish is a deep, vague unease with no clear cause, while anxiety is worry about a specific choice.
From the Discourses
Passages where Osho speaks to this question — each links to the complete discourse.
Question: OSHO, WHAT IS ANGUISH? IS IT JUST ANOTHER NAME FOR ANXIETY? You cannot be decisive, certain. The other man may look bigger, that is a certainty, but a smaller man may be more sharp, more clever, more cunning, may have known aikido, judo, jujitsu, and who knows what. The stronger man may not know anything, may be just a heavyweight, not a heavyweight champion, and the smaller man may throw him off. We are not programmed. Dogs are programmed and they can read each other's program easily. They give all the signs of their program: "This is what I can do. These are my teeth, you can see them. This is my bark, this way I jump, this way I will hit. You show YOURSELF." They both put their cards on the table. And when you see that one person has all the great cards, what is the point...?
Question: BELOVED OSHO, WHAT IS AGONY AND WHAT IS ECSTASY? I told my parents, "Please let me go. I am not going to project anything for my future. I want to keep it open so if nature desires anything of me, I am available. If nothing is desired of me that too is perfectly good. Who am I to expect that something should be desired of me? One day I was not, one day I will not be. Just a few days in between -- why make much fuss about it? Can't you pass silently across this little interval between birth and death without making noise, raising flags, and shouting slogans? Can't you simply pass?" But they said, "This is not the way. Everybody has to have an ideal; otherwise he will be lost.
Beloved Osho, why is it so difficult to get rid of pain, misery, suffering or anguish, while knowing perfectly well that one has just to understand and drop them?
Your suffering makes you somebody special. Without all your suffering, you are nobody. Who are you? You will not even have something to talk about with anybody. You will be at a loss -- what are you going to talk about? In England, people talk about the weather just to avoid real conversation. It is a very sophisticated way, to talk about weather. But it looks a little idiotic because you are seeing the weather, I am seeing the weather, it makes no sense to say, "What a beautiful day, how sunny!" you are seeing it, you are also in the same day. You are not tomorrow, you are not yesterday, you are here with me. And you say, "Yes, so beautiful!" This is because of the English character; it is one of the most phony characters in the world. It does not want to raise any controversial conversation. Politics…