Question: Are both Azadirachta and Maihuenia part of the cactus family?

Context articles: Coryphantha alversonii
Azadirachta
Maihueniopsis
Mammillaria
Echinocereus dasyacanthus
Rat tail cactus
Azadirachta indica
Echinocereus reichenbachii
Parodia scopa
Maihuenia

Coryphantha alversonii, commonly known as the foxtail cactus, is a stem succulent plant in the Coryphantha genus of the cactus family (Cactaceae).
Azadirachta is a genus of two species of trees in the mahogany (Meliaceae) family.
 Numerous species have been proposed for the genus but only two are currently recognized, "Azadirachta excelsa" and the economically important tree "Azadirachta indica".
 The latter is informally called the Neem tree; see also Neem oil.
 Both species are native to the Indomalaysian region, and "A. indica" is also widely cultivated and naturalized outside its native range.
Maihueniopsis (from Greek "opsis", "view", referring to its resemblance to the unrelated "Maihuenia") is a genus of the cactus family (Cactaceae), containing 18 species.
The genus Mammillaria is one of the largest in the cactus family (Cactaceae), with currently 200 known species and varieties recognized.
 Most of the mammillarias are native to Mexico, but some come from the southwest United States, the Caribbean, Colombia, Venezuela, Guatemala and Honduras.
 The common name "pincushion cactus" refers to this and the closely related genus "Escobaria".
Echinocereus dasyacanthus is a member of the cactus family, Cactaceae.
 It is one of about 2000 total species belonging to this family.
 The cactus is commonly known as Texas rainbow cactus because of the subtle rings or bands of contrasting colors along the stem of the plant.
 Not all Texas rainbow cacti have the "rainbow" coloration on their stems.
 Another common name is spiny hedgehog cactus.
Rat tail cactus is the common name for several members of the cactus family:
Azadirachta indica (commonly known as neem, nimtree and Indian lilac) is a tree in the mahogany family Meliaceae.
 It is one of two species in the genus "Azadirachta", and is native to the Indian subcontinent, i.e. India, Nepal, Pakistan, Bangladesh, Sri Lanka, and Maldives.
 It typically is grown in tropical and semi-tropical regions.
 Neem trees now also grow in islands located in the southern part of Iran.
 Its fruits and seeds are the source of neem oil.
Echinocereus reichenbachii (commonly known as lace or hedgehog cactus) is a perennial plant and shrub in the cactus family.
 The species is native to the Chihuahuan Desert and parts of northern Mexico and the southern United States, where they grow at elevations up to 1500 meter .
 The scientific name, "Echinocereus", comes from the Greek "ekinos", meaning hedgehog, and "cereus", the Latin term for wax paper.
 The specific epithet honors German botanist Ludwig Reichenbach.
 This cactus earned the Royal Horticultural Society's Award of Garden Merit.
Parodia scopa syn.
 "Notocactus scopa" (silver ball cactus) is a species of flowering plant in the cactus family Cactaceae, native to upland southern Brazil and Uruguay.
 It is a ball- or cylinder-shaped cactus growing to 5 - tall by 10 cm broad, with a spiny, woolly crown and pale yellow flowers in summer.
Maihuenia is a genus of cactus (family Cactaceae) and the sole genus of the subfamily Maihuenioideae, which is the smallest subfamily of the Cactaceae.
 The genus comprises two cushion-forming, mucilaginous species.
 They are found at high elevation habitats of Andean Argentina and Chile.