Question: Equisetum and Cryptotaenia, are plants?

Context articles: Equisetopsida sensu lato
Cryptotaenia
Equisetum dimorphum
Mixed-linkage glucan
Equisetum
Calamites
Richard L. Hauke
Equisetopsida

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..."
Cryptotaenia, also honewort, is a genus of two species of herbaceous perennial plants, native to North America, Africa, and eastern Asia, growing wild in moist, shady places.
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
Mixed-linkage glucan (MLG), sometimes incorrectly referred to as beta-glucan, is a hemicellulosic polysaccharide consisting of β-D(1-3) and β-D(1-4) linked glucosyl residues.
 MLG is highly prevalent within the Poales, where it has important properties in the diet.
 In addition, although thought to be confined to the Poales, MLG has been found to be highly prevalent in plants of the distantly related genus "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.
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 . )
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Richard L. Hauke (1930-2017) was for many years a Professor of Botany at the University of Rhode Island in Kingston, Rhode Island.
 He was considered one of the world's leading experts on the plants known as horsetails ("Equisetum" spp.)
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.