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.
Algae
Some parasitic algae (e.g., the green algae "Prototheca" and "Helicosporidium", parasites of metazoans, or "Cephaleuros", parasites of plants) were originally classified as fungi, sporozoans, or protistans of "incertae sedis", while others (e.g., the green algae "Phyllosiphon" and "Rhodochytrium", parasites of plants, or the red algae "Pterocladiophila" and "Gelidiocolax mammillatus", parasites of other red algae, or the dinoflagellates "Oodinium", parasites of fish) had their relationship with algae conjectured early. In other cases, some groups were originally characterized as parasitic algae (e.g., "Chlorochytrium"), but later were seen as endophytic algae. Some filamentous bacteria (e.g., "Beggiatoa") were originally seen as algae. Furthermore, groups like the apicomplexans are also parasites derived from ancestors that possessed plastids, but are not included in any group traditionally seen as algae.