Question: Are the Sternbergia and Echinopsis genuses of plants both native to the same regions?

Context articles: Sternbergia vernalis
Echinopsis backebergii
Sternbergia
Sternbergia colchiciflora
Echinopsis scopulicola
Narcisseae
Sternbergia pulchella
Echinopsis
Echinopsis pachanoi
Echinopsis peruviana

Sternbergia vernalis is a bulbous flowering plant in the family Amaryllidaceae, subfamily Amaryllidoideae, which is sometimes used as an ornamental plant.
 It has yellow flowers which appear in spring.
 The species is native to central and southwestern Asia (Turkmenistan, Tajikistan, Uzbekistan, Armenia, Azerbaijan, Georgia, Iran, Iraq, Lebanon, Syria and Turkey).
Echinopsis backebergii is a species of flowering plant in the cactus family Cactaceae, native to eastern Bolivia and southern Peru.
 It grows to 5 cm tall and wide, with single or clustered globose stems 4-5 cm thick, with about 15 ribs and covered in grey-brown spines.
 Large, showy, carmine-red flowers are borne in summer.
 As the minimum temperature requirement is 10 C , in temperate regions it must be grown under glass with heat.
Sternbergia is a genus of Eurasian and North African plants in the Amaryllis family, subfamily Amaryllidoideae.
Sternbergia colchiciflora is a bulbous flowering plant in the family Amaryllidaceae, subfamily Amaryllidoideae, which is sometimes used as an ornamental plant.
 The species is native to southern Europe from Spain to Ukraine, as well as from Morocco, Algeria, Turkey, Syria, Lebanon, Palestine, Iran and the Caucasus.
 It has yellow flowers which appear in autumn.
Echinopsis scopulicola is a type of cactus native to Bolivia, which contains psychedelic compounds.
 Many claim this species contains mescaline, which was until recently unconfirmed due to the lack of official research, but a study published in September 2010 by the International Society for Ethnopharmacology placed it in the top third of the results for their samples.
 This included 14 taxa/cultivars of the subgenus Trichocereus of the genus Echinopsis, with Scopulicola noted to contain 0.82% mescaline/dry weight in the outer green layer.
Narcisseae is a small tribe of plants belonging to the subfamily Amaryllidoideae of the Amaryllis family (Amaryllidaceae), where it forms part of the Eurasian clade, and is one of three tribes in the European (Mediterranean) clade.
 It contains two genera ("Narcissus" and "Sternbergia") and approximately 58 species, but probably also "Lapiedra".
 The two genera are distinguished from each other by the presence of a paraperigonium in the former.
Sternbergia pulchella is a bulbous flowering plant in the family Amaryllidaceae, subfamily Amaryllidoideae.
 It has yellow flowers which appear in autumn.
 The species is native to Syria and Lebanon.
Echinopsis is a large genus of cacti native to South America, sometimes known as hedgehog cactus, sea-urchin cactus or Easter lily cactus.
 One small species, "E. chamaecereus", is known as the peanut cactus.
 The 128 species range from large and treelike types to small globose cacti.
 The name derives from "echinos" hedgehog or sea urchin, and "opsis" appearance, a reference to these plants' dense coverings of spines.
Echinopsis pachanoi (syn.
 Trichocereus pachanoi) — known as San Pedro cactus — is a fast-growing columnar cactus native to the Andes Mountains at 2000 – in altitude.
 It is found in Argentina, Bolivia, Chile, Ecuador and Peru, and it is cultivated in other parts of the world.
 Uses for it include traditional medicine and traditional veterinary medicine, and it is widely grown as an ornamental cactus.
 It has been used for healing and religious divination in the Andes Mountains region for over 3,000 years.
 It is sometimes confused with its close relative "Echinopsis peruviana" (Peruvian torch cactus).
Echinopsis peruviana (syn.
 Trichocereus peruvianus), Peruvian torch cactus, is a fast-growing columnar cactus native to the western slope of the Andes in Peru, between about 2000 - above sea level.
 It contains the psychoactive alkaloid mescaline as well as other alkaloids, although reported levels vary considerably and do not approach the concentrations found in "Echinopsis pachanoi".