Grace is in a great measure a natural gift; elegance implies cultivation; or something of more artificial character. A rustic, uneducated girl may be graceful, but an elegant woman must be accomplished and well trained. It is the same with things as with persons; we talk of a graceful tree, but of an elegant house or other building. Animals may be graceful, but they cannot be elegant. The movements of a kitten or a young fawn are full of grace; but to call them "elegant" animals would be absurd.
Richard Whately