Palm grass -
Molineria capitulata is a species of flowering plant known by the common name palm grass. It is native to much of eastern and southern Asia, Indonesia, and northern Australia. It can be found in many other tropical and warmer temperate places, where it is grown as an ornamental plant. This is a bunch-forming herb with long, flat, fibrous leaves and star-shaped yellow flowers. The fibers from the plant have been used for purposes such as making nets, and the fruit is edible.
Palm
The Arecaceae are a botanical family of perennial lianas, shrubs, and
trees commonly known as palms. (Due to historical usage, the family is alternatively called Palmae or Palmaceae.[3]
Tree-
In botany, a tree is a perennial plant with an elongated stem, or trunk, supporting leaves or branches.
In some usages, the definition of a tree may be narrower, including only woody plants, only plants that are usable as lumber or only plants above a specified height. At its broadest, trees include the
taller palms, the tree ferns, bananas and bamboo.
Grass-
Grasses, or more technically graminoids, are monocotyledonous, usually herbaceous plants with narrow leaves growing from the base. They include the "true grasses", of the family Poaceae (also called Gramineae), as well as the sedges (Cyperaceae) and the rushes (Juncaceae). The true grasses include cereals, bamboo and the grasses of lawns (turf) and grassland. Sedges include many wild marsh and grassland plants, and some cultivated ones such as water chestnut (Eleocharis dulcis) and papyrus sedge (Cyperus papyrus).
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Wikipedia
The cause of confusion I believe is because of the fact palms and grasses are both monocots, while most 'trees' are dicots. Another reason may be lack of a cambium a state both of them suffer being monocots, but is not a sufficient condition being a property of a higher taxa.
Grasses are from family Poaceae while palms are family Arecaceae.
IMO let's stick to plants or just palms