Pagan comes from the Latin word Paganus, which means country-dweller. Since Pagan's original definition was country-dweller and those in the country worship spirits of nature, the term Pagan has come to mean any religion that honors nature. That includes but is not limited to, Wicca, Hellenism, Hinduism, Shintoism, and some may argue Satanism.
Wicca is a religion, which was started somewhere around 1950(I think) by Gerald Gardner. Although Wicca is a relatively younger religion, it's practices and beliefs date back to Greece, Roman, and the Celtics. Wicca is a sometimes classified as a neopagan religion, meaning a new Pagan religion.
Witchcraft is the practice of magick. It encompasses prayer and spellwork. Witchcraft is often viewed as a religion of its own. However most if not all religions have some type of witchcraft in them. Training an animal or making an herbal tea from scratch can also be classified as witchcraft.