Are the words distress, and stress interchangeable? I have heard them used in the same place, but are they the same?
He was very (stressed/distressed) about his co-workers thoughts of his idea.
There are indeed some contexts where either word could be used, but they mean different things. In other words, the two words are (or rather, can be) grammatically interchangeable, but not semantically.
He was very stressed about what his co-workers thought of his idea.
This means he was feeling tension, strain, and/or worry about what his colleagues thought. It's even possible (unlikely, but possible) that his co-workers approved of his idea — perhaps approval means more work for him, or something. See definition 2 or 4 here.
He was very distressed about what his co-workers thought of his idea.
This means that he was outright upset by his co-workers disapproval: their negative opinions caused him psychological suffering.
As you can see, at least in this particular case, the difference between the words is kinda-sorta one of degree: distress is a worse feeling than stress. But there are other differences: for example, you can be "under stress", but you can't be "*under distress".
No, they are not. "Stress" (in this usage), means "psychological tension".
"Distress" is anxiety, sorrow, or pain.
While one can be stressed and distressed at the same time, it is not always necessary. Simplest example: "Damsel in distress" is never "Damsel under stress"
In the context here, I'd say 'Stress' is meant as defined by the NHS, meaning "the feeling of being under too much mental or emotional pressure." and distress, as defined by dictionary.com, means "great pain, anxiety, or sorrow; acute physical or mental suffering; affliction; trouble." (there are other definitions for both words).
Under these definitions, there may be cases where the two words are interchangeable. However, for the most part they do mean slightly different things.
To use your example, to say "He was very stressed by his co-workers thoughts about his idea" would indicate that the man in question was maybe worried by his colleague's thoughts and felt put under pressure by them, but "He was very distressed by his co-workers thoughts about his idea" would mean that he was very upset and/or hurt by them.
Whilst the two sentences still have broadly similar meanings, the second sentence is a lot stronger than the first. Therefore, although both would make sense, 'stress' and 'distress' aren't entirely interchangeable here.