Answer:
Crows and ravens are in the same genus, "corvus," and are similar in more ways than they are different. Ravens are larger and have heavier bills and deeper voices than crows. Ravens are non-migratory and tend to be found in northern and mountainous environments in North America whereas crows are more widespread and may migrate in and out of Canada. Ravens are known to be one of the smartest animals because they are able to make and use tools and can learn to do something just by watching another raven.
See the related link for a great comparison of the two birds.
The difference between a rave and a crow is:
Raven:
The Raven is larger and average 25" tall (64 cm) with a four foot (122 cm) wing span and the beak is more slender and slightly longer than a crows. A raven's feathers shine with blue and purple tints when the sun hits them. The Raven's tail when spread meets at a triangular point.
Crow:
Crows are smaller and approximately 18" (46 cm) tall and their wing span is three feet (91 cm), similar to a dove. The beak is slightly thicker than a ravens. A crows feathers are flint black, may have lighter markings and duller than a ravens feathers. Crows can fluff their feathers into a mane and the tail curves evenly like a seashell.