Spores and seeds are alike in that plants produce them both to disperse their progeny, allowing new organisms to grow in different locations than their parental organisms. They are different in that spores are very small, single-celled structures, while seeds are relatively large and protected with a seed coat.
Due to their small size and light weight, spores, such as those produced by ferns and horsetails, can be carried long distances by the wind. This allows these types of plants to disperse efficiently, but some spores can easily wind up in areas that are not appropriate for survival. Spores only have one copy of each of the plant's chromosomes, and grow into a small plant stage known as a gametophyte. These release and receive gametes. Once fertilized, the eggs grow in place into the larger sporophyte, which has two copies of each chromosome. They then release the spores.
Seeds are much larger and heavier than spores due to their seed coats. These not only protect the plant embryos, but also provide them with their first source of nutrition. The embryo in a seed has two copies of each chromosome, and it grows into a large sporophyte. The spores of seed plants are retained in the plant, however, and grow into reproductive structures such as flowers, which then form seeds once fertilized.