Elaeagnus angustifolia - Russian olive. Flowers early summer, fruit ripe in autumn, leaves have Willow leaf shape, very glaucous, very rough black bark on mature trees. Incredibly cold hardy.
Elaeagnus umbellata - autumn olive, leaves with wavy margin, very fragrant flowers spring, from leaf axils along length of previous year's growth. Brown speckled with silver fruit ripens after autumn equinox (typically). Fruit tends to be dry, thin layer of very tart, almost cherry flavor flesh. Seed is soft, easily chewed, with a mild nutty flavor. Too dry to be very tasty for out of hand eating. Very cold hardy, thru zone 4.
Elaeagnus multiflora - goumi berry sometimes also called autumn olive. Larger, more fleshy, better tasting fruit than E umbellata. Fruit is more red color, umbellata is more a speckled brown. Fruit does have fine silver spots, but less conspicuous than umbellata, overall fruit looks more red. Fragrant flowers in spring, leaf axils along length of previous year's growth. Usually fruit is ripe before autumnal equinox. There's some overlap with umbellata, but not much. Hardy thru zone 6 into zone 5, at least 5b, maybe 5a.
Elaeagnus pungens - thorny silver berry, goumi ( fruit) Japanese silverberry, autumn olive. This is not as winter hardy as above, typically only zone 7 hardy. This is the silverberry most often used by Japanese for bonsai. Fragrant flowers in autumn, fruit ripens over winter usually ripe middle or late spring, early summer. Fruit similar to multiflora, maybe slightly larger.
E. Ebbingii (pungens x macrophylla) select cultivars have variegated leaves. Does not make the abundant fruit of species elaeagnus.
