It is quite common for Wicca and Celtic Paganism to be lumped together. Many people assume that they are the same thing. They are not. Here are the key differences between the two practices as outlined by this article.
Wicca is a relatively modern religion. Celtic Pagan Reconstructionism attempts to practice their spirituality as the Celts did during their Golden Age: Between 400-1300 AD.
Wicca breaks the universe down into the four Greco-Roman elements: Earth, Air, Wind and Fire.
Celtic Paganism adheres to the ancient Celtic view that the universe is triunal in nature. The world is composed of Air, Land and Sea. Existence is also made up of three realms: This world, the other world and the underworld.
Wicca is based on the idea that you should harm none. This tenet is different from the views of the Celts, who in general were a warrior culture. They believed that it was necessary sometimes to kill in order to survive and that death and life were interconnected.
Wicca breaks down the deities into the God/Goddess dynamic. For example, there is little difference between Osiris and Odin – they just are invoked for different purposes. Celtic Paganism believes that each deity is individualistic and unique.
Celtic Paganism recognizes that sacred places are found, not created.
Of course it must be said that most of what we know about the Celts is an educated guess, since they did not keep written records about themselves. Spiritual knowledge was passed on orally in the Celtic Tradition. Also, many Celtic artifacts were destroyed by the Romans, Vikings and Christians.
However, the distinguishing feature of Reconstructionalist Celtic Paganism is that it is an attempt to practice a spirituality that is close to that of the Ancient Celts. While Wicca is a modern, New Age creation with Celtic elements.