I would like to know the meaning that comes to your mind when you hear the four words as a native speaker. If you don't know the difference between two of the words, please let me know instead of googling or searching a dictionary. I would like to know how native speakers (naturally) think of those words.
It would be better if the answer is based on the American accent.
One more thing, Should I say: "Two pieces of pepper." or "two pieces of peppers" (with an S for plural).
Edit: After reading the related questions in the comments section, I think the word "Pepper" is commonly used by Americans no matter what the shapes are. I guess you say "Bell pepper" instead of Capsicum and I feel that Capsicum is the scientific name (not common). I don't know if u say "Chilli" or maybe you say "Hot pepper" cuz you love saying the word "Pepper".