Question: Are Flax and Calamus in the same family?

Context paragraphs:
Calamus (palm): Calamus is a genus of the palm family Arecaceae.  These are among several genera known as rattan palms.  There are an estimated 400 species in this genus, all native to tropical and subtropical Asia, Africa, and Australia.  They are mostly leaf-climbing lianas with slender, reedy stems.  To aid scrambling some species have evolved hooks on the underside of the midrib, or more commonly by modified "pinnae" or tendrils in the form of stout, backward-pointing spines.  These stems may grow to lengths of 200 metres.

Knobbed porgy: The knobbed porgy, "Calamus nodosus", is an ocean-going species of gamefish of the Sparidae (Bream/Porgy family).  They are only found in the western portion of the tropical Atlantic Ocean, where they are often caught with trawling nets or by angling, and used as food.  The Knobbed porgy was named by John Randall and David Caldwell as part of a 1966 review of the "Calamus" genus, which was published in the academic journal "Science".  Randall and Caldwell also described three other species of "Calamus" in the paper.

Phormium: Phormium is a genus of two plant species in the Asphodelaceae family.  One species is endemic to New Zealand and the other is native to New Zealand and Norfolk Island.  The two species are widely known in New Zealand as 'flax' and elsewhere as New Zealand flax or flax lily but are not related to flax, which is native to the region extending from the eastern Mediterranean to India and which was used by humans in 30,000 B.C.

Flax: Flax (also known as common flax or linseed), "Linum usitatissimum", is a member of the genus "Linum" in the family Linaceae.  It is a food and fiber crop cultivated in cooler regions of the world.  The textiles made from flax are known in the Western countries as linen, and traditionally used for bed sheets, underclothes, and table linen.  The oil is known as linseed oil.  In addition to referring to the plant itself, the word "flax" may refer to the unspun fibers of the flax plant.  The plant species is known only as a cultivated plant, and appears to have been domesticated just once from the wild species "Linum bienne", called pale flax.

Hesperolinon drymarioides: Hesperolinon drymarioides is a rare species of flowering plant in the flax family known by the common names drymary dwarf flax and drymaria-like western flax; it is named for its resemblance to genus "Drymaria".  It is endemic to California, where it grows in the central inland North Coast Range.  Most of the few known occurrences have been noted in Lake County.  It is a plant of serpentine soils in chaparral and woodland ecosystems.  This is a small annual herb growing a thin branching brown stem low to the ground or erect to about 20 centimeters in height.  Leaves appear in whorls of four on the lower part of the stem and are dark reddish green with plentiful glandular hairs.  Its flowers have light pink-veined white petals in a corolla about a centimeter across.  Protruding stamens hold large yellow or purplish-white anthers.

Hesperolinon adenophyllum: Hesperolinon adenophyllum is a rare species of flowering plant in the flax family known by the common names glandular dwarf flax and glandular western flax.  It is endemic to California, where most known occurrences have been recorded in Lake and Mendocino Counties.  It is generally found in chaparral ecosystems on serpentine soils.  This is an annual herb growing erect to heights between 10 and 50 centimeters.  Its narrow, lance-shaped leaves are lined with rows of teeth with large knobby glandular points.  The flower has small sepals speckled with glandular hairs and five thin yellow petals.  The stamens protrude from the face of the flower and hold large yellow anthers.

False flax oil: False flax oil is a pressed seed oil, derived from the "Camelina sativa" or "false flax", also called "gold of pleasure".  False flax has long been grown in Europe, and its oil used as a lamp oil until the 18th century.  In recent times, it has been explored for use in cosmetic and skin care products.It has a high content of omega-3 and is used as a food supplement by some cultures.  In the United States the Food and Drug Administration has not rated the oil for human consumption yet.  False flax belongs to the "Brassicaceae" (mustard and cabbage) family, which also contains many other seed oil plants, such as rapeseed oil.  It contains 1–3% erucic acid.

Hesperolinon tehamense: Hesperolinon tehamense is a rare species of flowering plant in the flax family known by the common names Tehama County western flax and Paskenta Grade dwarf flax.  It is endemic to northern California, where it is known from only about ten occurrences, mostly within Tehama and Glenn Counties.  Most of its habitat is on Bureau of Land Management lands and within the Mendocino National Forest, in chaparral ecosystems with serpentine soils.  The plant produces thin, hairy stems up to 50 centimeters in maximum height with small, sparse linear leaves.  The inflorescence bears several small flowers with pale to bright yellow notched petals just a few millimeters long.

Hesperolinon serpentinum: Hesperolinon serpentinum (now "Hesperolinon sharsmithae") is a rare species of flowering plant in the flax family known by the common name Napa dwarf flax, or Napa western flax.  "Hesperolinon serpentinum" was not validly published by McCarten although it appears in the Jepson Manual (Hickman, 1993).  The species was validly published as "Hesperolinon sharsmithae" in 2006 by O'Donnell (Madroño 53:404–408).  The species is endemic to northern California, where it is known from fewer than twenty occurrences in four counties surrounding the San Francisco Bay Area.  It is a member of chaparral plant communities, generally on serpentine soils.  It produces a thin, erect stem up to 30 centimeters tall, with sparse flat, narrow leaves.  The inflorescence holds several light yellow flowers with petals only 2 or 3 millimeters long.  The plant is threatened mainly by development of its habitat.

Linum lewisii: Linum lewisii ("Linum perenne" var.  "lewisii") (Lewis flax, blue flax or prairie flax) is a perennial plant in the family Linaceae, native to western North America from Alaska south to Baja California, and from the Pacific Coast east to the Mississippi River (USDA Plant Profile: "Linum lewisii").  It grows on ridges and dry slopes, from sea level in the north up to 11000 ft in the Sierra Nevada.

Supporting paragraphs: Flax Calamus (palm)
Answer: no