Question: Are both Trichodiadema and Bursaria part of a plant genus?

Context articles: Banksia sessilis
Falconeria
Trichodiadema
Hesperelaea
Acanthopale
Ipheion
Bursaria spinosa
Aldrovanda vesiculosa
Bursaria
Phyllanthus

Banksia sessilis, commonly known as parrot bush, is a species of shrub or tree in the plant genus "Banksia" in the family Proteaceae.
 It had been known as Dryandra sessilis until 2007, when the genus "Dryandra" was sunk into "Banksia".
 The Noongar peoples know the plant as Budjan or Butyak.
 Widespread throughout southwest Western Australia, it is found on sandy soils over laterite or limestone, often as an understorey plant in open forest, woodland or shrubland.
 Encountered as a shrub or small tree up to 6 m in height, it has prickly dark green leaves and dome-shaped cream-yellow flowerheads.
 Flowering from winter through to late spring, it provides a key source of food—both the nectar and the insects it attracts—for honeyeaters in the cooler months, and species diversity is reduced in areas where there is little or no parrot bush occurring.
 Several species of honeyeater, some species of native bee, and the European honey bee seek out and consume the nectar, while the long-billed black cockatoo and Australian ringneck eat the seed.
 The life cycle of "Banksia sessilis" is adapted to regular bushfires.
 Killed by fire and regenerating by seed afterwards, each shrub generally produces many flowerheads and a massive amount of seed.
 It can recolonise disturbed areas, and may grow in thickets.
Falconeria is a monotypic plant genus in the family Euphorbiaceae, first described as a genus in 1839.
 The genus is sometimes included within the genus "Sapium".
 The sole species is Falconeria insignis.
 The plant is found from India, Nepal, Bangladesh, and Sri Lanka to Indochina, China (Hainan, Sichuan, Yunnan), Thailand and Peninsular Malaysia.
Trichodiadema is a genus of succulent plants of the family Aizoaceae.
Hesperelaea is a plant genus with only one species, probably now extinct.
 Hesperelaea palmeri was found only on Guadalupe Island, a small island in the Pacific Ocean, part of the Mexican state of Baja California, about 400 km southwest of Ensenada.
 The last collection of the plant on the island was in 1875, so the species and the genus must now be presumed extinct.
 An intensive search for the plant in 2000 was unsuccessful.
Acanthopale is a plant genus in the Acanthaceae plant family.
 The genus name is based on the classic Greek words for thorn "ákantha" and stake "palum".
 Some species in the genus are cultivated as ornamental plants.
The flowering plant genus Ipheion (starflower, spring starflower) belongs to Allioideae subfamily of the Amaryllidaceae family.
 The World Checklist of Selected Plant Families no longer recognize the genus, regarding it as a synonym of "Tristagma", although The Plant List accepts two species.
Bursaria spinosa is a small tree or shrub in the family Pittosporaceae.
 The species occurs in mainly in the eastern and southern half of Australia and not in Western Australia and the Northern Territory.
 Reaching 10 m (35 ft) high, it bears fragrant white flowers at any time of year but particularly summer.
 A common understory shrub of eucalyptus woodland, it aggressively colonises disturbed areas and fallow farmland.
 It is an important food plant for several species of butterflies and moths, particularly those of the genus "Paralucia".
Aldrovanda vesiculosa, commonly known as the waterwheel plant, is the sole extant species in the flowering plant genus "Aldrovanda" of the family Droseraceae.
 The plant captures small aquatic invertebrates using traps similar to those of the Venus flytrap.
 The traps are arranged in whorls around a central, free-floating stem, giving rise to the common name.
 This is one of the few plant species capable of rapid movement.
Bursaria is a genus of large shrubs and small trees which are native to Australia.
 The genus was first described by Antonio Cavanilles in 1797, with his description of the type species "B. spinosa".
 The name is derived from the Latin word "bursa" (purse) which relates to the shape of its seed capsules.
Phyllanthus is the largest genus in the flowering plant family Phyllanthaceae.
 Estimates of the number species in this genus vary widely, from 750 to 1200.
 "Phyllanthus" has a remarkable diversity of growth forms including annual and perennial herbs, shrubs, climbers, floating aquatics, and pachycaulous succulents.
 Some have flattened leaflike stems called cladodes.
 It has a wide variety of floral morphologies and chromosome numbers and has one of the widest range of pollen types of any seed plant genus.