Question: Do the genuses Anemone and Arachniodes belong to the same family?

Context articles: Stichodactyla helianthus
Phymanthus crucifer
Heteractis aurora
Anemone
Urticina columbiana
Metridium dianthus
Anemone hupehensis
Arachniodes
Sebae anemone
Actinodendron arboreum

Stichodactyla helianthus is a sea anemone of the family Stichodactylidae.
 "Helianthus" stems from the Greek words ἡλιος (meaning sun), and ἀνθος, meaning flower.
 "S. helianthus" is also referred to as the 'sun anemone'.
 "S. helianthus" is a large, green, sessile, carpet-like sea anemone, from the Caribbean.
 It lives in shallow areas with mild to strong currents.
 The anemone crab ("Mithraculus cinctimanus") is often associated with it, being found among the tentacles or on the column and margin of the oral disc, as is the sun anemone shrimp.
Phymanthus crucifer, commonly known as the rock flower anemone, flower anemone, red beaded anemone or the beaded anemone, is a species of sea anemone in the family Phymanthidae.
 It has been described as "closely similar" to "Heteractis aurora" in several ways, commonly exhibiting "tentacles with swollen cross-bars" bearing large clusters of stinging nematocysts. However, "P. crucifer" may also be found with smooth tentacles, sometimes in the immediate vicinity of a swollen-crossbarred specimen.
Heteractis aurora, also known as the beaded sea anemone, aurora host anemone, sand anemone, carpet anemone, flat anemone, corn anemone, ritteri anemone, saddle tip anemone, adhesive sea anemone, and the white beaded anemone, is a species of sea anemone in the family Stichodactylidae.
Anemone is a genus of about 200 species of flowering plants in the family Ranunculaceae, native to temperate zones.
 The genus is closely related to "Pulsatilla" ('Pasque flower') and "Hepatica"; some botanists even include both of these genera within "Anemone".
Urticina columbiana, common names crusty red anemone, Columbia sand anemone, sand anemone, and the sand-rose anemone, is a species of sea anemone in the family Actiniidae.
Metridium dianthus, common name the plumose anemone or frilled anemone, is a species of sea anemone in the family Metridiidae.
 It is found in the seas off northwest Europe and the east and west coasts of North America.
 This anemone is perhaps better known by its synonym, Metridium senile; but that name is now considered invalid.
Anemone hupehensis, Anemone hupehensis" var.
 "japonica, and Anemone" × "hybrida (commonly known as the Chinese anemone or Japanese anemone, thimbleweed, or windflower) are species of flowering herbaceous perennials in the Ranunculaceae family.
Arachniodes is a fern genus in the family Dryopteridaceae (wood ferns).
The sebae anemone("Heteractis crispa"), also known as leathery sea anemone, long tentacle anemone or purple tip anemone, is a species of sea anemone belonging to the Stichodactylidae family native from the Indo-Pacific area.
Actinodendron arboreum, common name the tree anemone and hell's fire anemone, is a species of sea anemone in the family Actinodendronidae.
 It is native to the Indo-Pacific where it grows at depths of down to 28 m .
 Most sea anemone species are harmless to humans, but "A. arboreum" is highly venomous and its sting can cause severe skin ulcers (as also suggested by its alternative name, hell's fire anemone).