Question: Are Equisetum and Vallea both a type of genus?

Context paragraphs:
Equisetum dimorphum: Equisetum dimorphum is an extinct horsetail species of the Equisetaceae family, and one of the oldest records of the Equisetum genus.  It was found in rocks from the Lower Jurassic of Chubut, Argentina, among other plants as ferns, conifers and pteridosperms.  Their remains consist on stems, leaves, strobili, and pagoda structures, which are preserved as impressions and casts.  The combination of fine grained sediment, and the probable silica deposits in the epidermis of the plant, have managed to conserve not only its gross morphology, but also epidermal details not often present in this kind of preservation.  This species was described in 2015 in Ameghiniana by a team led by Andres Elgorriaga, that included investigators of the Museum of Paleontology Egidio Feruglio, the Swedish Museum of Natural History, and the Buenos Aires University

List of longest vines: This is a list of world's longest vines.  A vine can refer to any plant with a growth habit of trailing or (that is, climbing) stems or runners.  The first five species are unlikely to be superseded or even to change order of rank.  This list is not all inclusive in part because many species have never been measured, and also because more careful measurements are needed for many species on this list.  Some species have been included because they are the largest of a habit type (such as Poison Oak as longest root climber) or as the longest member of their division or phylum (such as Equisetum giganteum).

Equisetum scirpoides: Equisetum scirpoides (dwarf scouring rush or dwarf horsetail) Michx. , Fl.  Bor.-Amer.  2: 281 (1803).  2 n = 216."  "The smallest of the currently occurring representatives of the genus "Equisetum" (horsetail).

Equisetum ramosissimum: Equisetum ramosissimum , known as branched horsetail, is a species of evergreen horsetail (genus "Equisetum", subgenus "Hippochaete").  It is not the same species as "Equisetum ramosissimum" , which is a synonym of "Equisetum giganteum".

Equisetum: Equisetum ( ; horsetail, snake grass, puzzlegrass) is the only living genus in Equisetaceae, a family of vascular plants that reproduce by spores rather than seeds.

Equisetopsida: Equisetopsida, or Sphenopsida, is a class of vascular plants with a fossil record going back to the Devonian.  They are commonly known as horsetails.  Living horsetails are represented by about twenty herbaceous species in the single genus "Equisetum".  They typically grow in wet areas, with whorls of needle-like branches radiating at regular intervals from a single vertical stem.

Equisetum thermale: Equisetum thermale is an extinct horsetail species in the family Equisetaceae described from a group of whole plant fossils including rhizomes, stems, and leaves.  The species is known from Middle to Late Jurassic sediments exposed in the province of Santa Cruz, Argentina.  It is one of several extinct species placed in the living genus "Equisetum".

Equisetopsida sensu lato: Equisetopsida is the name of a class of plants that traditionally contains the single genus "Equisetum" (horsestails).  However, in 2009, in an article titled "A phylogenetic classification of the land plants to accompany APG III," Mark W. Chase and James L. Reveal proposed a much broader sense for the Equisetopsida class name.  In their system, Equisetopsida includes all land plants (embryophytes).  Their rationale was that "If the major clades of green algae are recognized as classes, then all land plants, the embryophytes, should be included in a single class..."

Vallea: Vallea is a genus of trees in the family Elaeocarpaceae.  Trees in this genus are native to the Andes mountain range in South America and are classified in two species:

Calamites: Calamites is a genus of extinct arborescent (tree-like) horsetails to which the modern horsetails (genus "Equisetum") are closely related.  Unlike their herbaceous modern cousins, these plants were medium-sized trees, growing to heights of more than 30 meters (100 feet).  They were components of the understories of coal swamps of the Carboniferous Period (around ERROR!  Start of period Carboniferous unknown, perhaps because it was mis-spelt or because it is missing from . ) .

Supporting paragraphs: Equisetum Vallea
Answer: yes