Seaweed
"Seaweed" is a colloquial term and lacks a formal definition. A seaweed may belong to one of several groups of multicellular algae: the red algae, green algae, and brown algae. As these three groups do not have a common multicellular ancestor, the seaweed are in a polyphyletic group. In addition, some tuft-forming bluegreen algae (Cyanobacteria) are sometimes considered to be seaweed.
Wakame
In Old Japanese, "me" stood for edible seaweeds in general as opposed to "mo" standing for algae. In kanji, such as 海藻, 軍布 and 和布 were applied to transcribe the word. Among seaweeds, wakame was likely most often eaten, therefore "me" especially meant wakame. It expanded later to other seaweeds like kajime, hirome (kombu), arame, etc. Wakame is derived from "waka" + "me" (若布, lit. young seaweed). If this "waka" is a eulogistic prefix, same as the "tama" of tamagushi, wakame likely stood for seaweeds widely in ancient ages. In Man'yōshū, in addition to 和可米 and 稚海藻 (both are read as "wakame"), "nigime" (和海藻, soft wakame) can be seen. Besides, "tamamo" (玉藻, lit. beautiful algae), which often appeared in Man'yo-shu, may be wakame depending on poems.