Ceremonial magic is a type of magic that depends heavily on book learning; precise, complicated ritual; and intricate sets of correspondences. In the West, ceremonial magic has been almost entirely rooted in Judeo-Christian myth until the late 19th century, and even today many ceremonial magicians continue to work within that context.
Ceremonial magic is also high magic. It is meant to have a spiritual purpose rather than a practical one, although there could be some overlap in those two concepts. It involves improving the soul, which might include gaining divine knowledge, purification, attraction of proper influences, and embracing one's destiny.
Folk magic historically is the magic of the common folk and has all manner of practical purposes: healing, attracting luck or love, driving away evil forces, finding lost items, bringing good harvests, fertility. Records of these practices are largely non-existent since practitioners were generally illiterate. Rituals were simple and probably evolved over time. They involved everyday items: plant material, coins, nails, wood, and so forth.
Folk magic is sometimes called low magic because if its practical nature and because of its association with the lower class.
Witchcraft is a highly problematic term today because of the different uses of the word today versus historically. In the West, many magical practitioners are now calling themselves witches and practice cross between ceremonial magic and folk magic. Workings are generally fairly simple, use common materials, and depend upon emotion and intent rather than exact ritual, but they may also borrow certain practices such as circle casting from ceremonial magic.
Historically, however, witchcraft meant malevolent magic, and that is the reason it was prosecuted. Witches were thought to kill, maim, cause sterility, blight crops, poison water, and bring general misfortune upon their targets.
Witches and folk magicians were two different groups of people. Most people identified as witches were also accused falsely, while folk magicians were valued members of their communities.