By strict definition, though plagiarism is not always copying, copying is always plagiarism. That is, copying is one form of plagiarism. The use of direct copying of someone else's words in your own work counts as plagiarism if you have not cited the origin of the copied words. Copying is plagiarism in the strictest sense, and there will be no debate as to whether a production that has been copied amounts to plagiarism.
The act of repackaging another's ideas as your own without giving credit to the original author is plagiarism. This is true whether done knowingly or not. If in addition to restating another's ideas you do so in a way that clearly mimics her style or exactly mimics her words, you are copying as well. In this sense, you can by copying and plagiarizing simultaneously, and others can justifiably state that you have copied and plagiarized the works of others.
Sometimes the acts of plagiarism and copying depend on your intent as a writer. It is possible that you have written something that completely originated from you alone, yet others find strong similarities between your work and that of previous authors. In this situation, you are neither copying nor plagiarizing because you had no intent to do so. Even if your style of writing is strikingly similar to that of another author's, without intent you technically have not committed copying or plagiarism.
You can restate that which is considered to be common knowledge in any manner without being guilty of copying or plagiarism. This even applies to direct copying. For example, restating a common statistical formula, such as the Central Limit Theorem, is not an example of plagiarism even if you did not cite the founder of that formula. In addition, you may copy it directly from a textbook without being accused of copying others' work.