A seedling is a tree that has been grown from a seed. A seedling often is not true to fruit (meaning that you will not necessarily get the same quality of fruit or nut). Without graft tissue, seedling trees are usually more winter hardy, grow more vigorously and may grow into much larger trees at maturity.
A grafted tree is a tree which has been reproduced to have consistent fruit quality and a controlled tree size (a cutting or bud from the “Mother tree” is joined to a rootstock). Grafted trees will always be true to fruit producing the same high quality as the superior Mother tree.