A difference exists.
Wiccans do spells because they believe in a sort of New Age “energy” which permeates the universe, and which has no will, and upon which intent can be passed along. This is, in my opinion, an attempt to explain mysteries in terms which adhere to this vague sort of submission to a New Age perception of quantum mechanics.
Christians, and also, the religions which predated it in the Roman Empire, endeavoured not to control or manipulate, but to enter into agreements with gods. If I light a candle to a god, and I petition him for something, and I agree that I will do something else in return, then I am not attempting to control them, but to exist in harmony with them.
Such an act, in my view, came to exist in Catholicism as well, where there are set standards of ritual contracts with the god of monotheism, in an attempt to plead with him to affect a persons life in a certain way. (The most basic is this: I will believe in the Church, and all of its Dogmas, and I will worship you and adhere to your law, if you in turn will save me from eternal punishment.)
Magic, the attempt to willfully change conditions by merit of inherit power, were frowned upon by both modern Christians, and the ancient, Classical polytheists. To both, we might assign the act of magic as being viewed as a symptom of great and profound hubris and impiety, and there is the assumption that natural order will prevail against such an imbalance.