Dry seed versus moist seed is a species by species decision. If ginkgo seed were to dry out the seed embryo would be killed, dead, the seed will not germinate. So moist ginkgo seed is good, the only type of ginkgo seed worth buying.
Pine tree seed, if moist will either germinate in transit or it will fungus and die. Dry pine seed is good.
I guarantee you if Sheffield's offers an option of wet or dry seed,, there is a reason. BUT there is no blanket reason I can give you, it is a species by species decision.
One more example. Japanese maple seed, often is offered wet or dry. Dry seed requires a warm stratification, which means for 3 months the seed should be moist and warm (50 F to 80 F). This treatment then needs to be followed by a 3 month cold stratification, where the seed is moist and cold. It should be timed so that the end of the second or cold stratification is about the ideal time for spring planting outside. After this the seed should sprout. The other method for dry maple seed is to plant dry seed in a flat sometime in early summer. Mark the flat well so you will know what is in it the following year. Then leave the flat outside all winter. In spring the seed will sprout. This is to be expected with dry maple seed and the seed of other species that need both a warm stratification and a cold stratification. Others are Carpinus, Ostrya, and a number of others.
If you purchase moist Japanese maple seed, that has not been dried out, and then immediately put it into cold moist stratification, the majority of the seed will sprout in spring without the need for a warm stratification. This means purchasing moist Japanese maple seed saves the grower 3 months of warm stratification and makes it easier planning the spring plant out because you don't have to have a flat of unsprouted, warm stratifying trees laying around until the next year.
So while browsing Sheffield's read the fine print on germination instructions. This will give you an idea how easy or difficult it will be to germinate the seed. Not all seed is as easy to grow as tomato seeds.