Question: Are both genera Leontopodium and Elaeagnus from the same family?

Context articles: Ithonidae
Ceraceopsora
Leontopodium microphyllum
Salix eleagnos
Elaeagnus
Edelweiss (song)
Leontopodium shinanense
Whip-lash squid
Elaeagnus pungens
Leontopodium

Ithonidae, commonly called moth lacewings and giant lacewings, is a small family of winged insects of the insect order Neuroptera.
 The family contains a total of ten living genera, and twelve extinct genera described from fossils.
 The modern Ithonids have a notably disjunct distribution, while the extinct genera had a more global range.
 The family is considered one of the most primitive living neuropteran families.
 Ithonids may be phytophagous.
 The family has been expanded twice, first to include the genus "Rapisma", formerly placed in the monotypic family Rapismatidae, and then in 2010 to include the genera that had been placed into the family Polystoechotidae.
 Both Rapismatidae and Polystoechotidae have been shown to nest into Ithonidae.
Ceraceopsora is a genus of rust fungi in the Chaconiaceae family.
 The genus is monotypic, containing the single species Ceraceopsora elaeagni, found in Japan growing on "Anemone flaccida" and "Elaeagnus umbellata".
Leontopodium microphyllum, known as Taiwan Edelweiss, or small leaf Edelweiss, is in the sunflower family (Asteraceae).
 It is endemic to the mountains of Taiwan.
Salix eleagnos the bitter willow, olive willow, hoary willow, rosemary willow, or elaeagnus willow, is a species of flowering plant in the family Salicaceae, native to central and southern Europe and south west Asia.
 Growing to 3 m tall by 5 m broad, it is an erect bushy deciduous shrub with narrow grey-green leaves up to 20 cm long, which turn yellow in autumn (fall).
 The green catkins, 3 - long, appear with the leaves in spring, male catkins having yellow anthers.
Elaeagnus , silverberry or oleaster, is a genus of about 50–70 species of flowering plants in the family Elaeagnaceae.
"Edelweiss" is a show tune from the 1959 Rodgers and Hammerstein musical "The Sound of Music".
 It is named after the edelweiss, a white flower found high in the Alps "(Leontopodium alpinum)".
 It was created for the 1959 Broadway production of "The Sound of Music" in the role originated by performer Theodore Bikel as a song for the character of Captain Georg Ludwig von Trapp.
 In the musical, Captain von Trapp and his family sing this song during the concert near the end of Act II as a statement of Austrian patriotism in the face of the pressure put upon him to join the navy of Nazi Germany following the Anschluss.
 It is also Captain von Trapp's subliminal goodbye to his beloved homeland, using the flower as a symbol of his loyalty to Austria.
 In the 1965 film adaptation, the song is also sung by the Captain earlier in the film when he rediscovers music with his children.
Leontopodium shinanense is a species of plant in the family Asteraceae.
 It is native to Japan and considered as a rare species by the IUCN since 1998.
The Mastigoteuthidae, also known as whip-lash squid, are a family of small deep-sea squid.
 Approximately 20 known species in six genera are represented, with members found in both the mesopelagic and bathypelagic zone of most oceans.
 Originally described by Verill in 1881, it was later lowered by Chun (1920) to a subfamily (Mastigoteuthinae) of the Chiroteuthidae.
 However, Roper et al. (1969) raised it back to the family level, and this has not been changed since.
 The taxonomy of this family is extremely unstable, and there have been at times one genus (Young, Lindgren, & Vecchione, 2008), two genera and four subgenera(Salcedo-Vargas & Okutani, 1994), two genera and several 'groups' (Salcedo-Vargas, 1997), five genera (Braid, McBride, & Bolstad, 2014) and one species with an uncertain placement, or six genera (Young, Vecchione, & Braid, 2014).
Elaeagnus pungens is a species of flowering plant in the family Elaeagnaceae, known by the common names thorny olive, spiny oleaster and silverthorn; also by the family name "oleaster".
 It is native to Asia, including China and Japan.
 It is present in the southeastern United States as an introduced species, a common landscaping and ornamental plant, and sometimes an invasive species.
Leontopodium is a genus of plants in the Asteraceae family (which also includes daisies and sunflowers).
 The genus is native to Europe and Asia.
 The fuzzy and somewhat stocky "petals" (technically, bracts) could be thought of as somewhat resembling lions' paws —hence the genus name combining "léōn" (lion) and "pódion" (foot).