What is the scientific name for seaweed?

Seaweed is a term mostly applied to some types of algae. It is not a scientific classification, but rather a colloquial term. The organisms may belong to quite different types of algae, and other organisms in the same groups may not be what we think of as seaweed. Thus their scientific names can be quite different from each other. Some examples:

Bladderwrack: fucus vesiculosus

Carrageen Mastocarpus stellatus