You cannot copyright an idea. You copyright an expression of that idea.
Copyright violation doesn't really have much to do with plagarism. If you copy someones work and distribute it without permission, that's copyright violation. If you take a chunk of someones work (e.g., a quote) and put it in your paper, and cite it, it is considered fair use and you do not violate copyright. I assume there are some other reasonable cases where you don't have to really cite the author because it's common knowledge where it came from (like if I said "I'll buy that for a dollar." you would know it came from RoboCop.)
Plagarism is where you put someones words or ideas down and do not give them credit. The point of plagarism is taking credit. If you put a quote down, word for word, and do not attribute it, then you have plagarized it. You have also done copyright violation in this case, but that is a side effect of stealing credit. Common knowlege statements do not need to be cited (if everyone knows gold is yellow, and Jane says it in a paper, you can say it too and not have to cite her).
You can plagarize ideas. If someone comes up with a novel idea or insight, and you parrot it as your own without attributing it, you are stealing credit for that person's idea. Plagarism. Again, I think there are some things that are so well known that you don't have to attribute them. When I talk here about Free Software, I don't have to cite Stallman. You guys know he came up with the idea.
Citing is good for other reasons. When you write a paper, you are building an ironclad case. Every citation is a fact supporting your case. When you cite, you give the reader the ability to backtrack through your argument, and give yourself credability.
