The major difference is that Galanthus (snowdrop) has three long petals and three shorter ones while Leucojum has 6 petals of equal length and yellow-green spots at the tips of the petals. (Such things are botanic divisions made of I note)
There are two different species you'll see in garden shops and they are different enough that I should treat them as two and not roll their growing needs into one lumped explanation. The two were talking about are Leucojum aestivum and Leucojum vernum
The flower on this early summer or late spring bloomer is white and you can expect to see the plant height reach 18-20 inches with the flowers carried well above the plant.
Plant the base of the bulb 3 inches deep and keep the bulbs 4 inches or so apart.
This bulb does best in a part shade garden. It does particularly well under deciduous shrubs (not evergreens) and trees.
It is an excellent cut flower.
It wants a moist spring environment and trying to grow it in the dry shade is a recipe for disaster. Moist soils are preferred so pond side is perfect.
Leucojum vernum or Spring snowflake
This plant blooms as soon as the frost is out of the ground it is one of the earliest bulbs in the garden appearing at least a month or more before the Summer snowflake
It is shorter by half than the Leucojum aestivum reaching 7-8 inches tall. Planting depths are the same 3 inches to the base of the bulb. And the growing needs of rich, fertile and damp soil is equally true.
While the L. vernum makes an excellent cut flower, it also has a slight fragrance that is missing in the Summer Snowflake.
Both bulbs will produce more and more flowers if left undisturbed.
Plant this bulb in a damp shade garden and it will give you spring bulbous blooms where most other bulbs will rot.
The Spring Snowflake is not offered for sale as often as the Summer Snowflake in most garden shops. So when you see them, pick up a few if you have the location to grow them.