Seaweed is a form of blue green algae and Spirulina is a single celled organism that is commonly classified as a type of blue green algae.
Blue green algae is a generic term for primitive single celled microscopic organisms that grow into colonies and therefore look like larger organisms. In actual fact these organisms are divided into 2 categories, the more primitive and much older organisms called cyanobacteria that includes Spirulina, it is not a true algae but a type of bacteria that feeds by photosynthesis, plants like algae evolved from these types of complex bacteria.
Seagreens is a seaweed which is a plant and therefore a true blue green algae. These are very different types of organisms, both are extremely rich in nutrients, more than any other edible organism but they are also a little different in nutritional content and have different benefits.
Spirulina, for example is easier to digest as it does not have a cell wall like plant, it is particularly rich in nutrients but especially high in protein and natural betacarotene.
Seagreens has enormous health benefits but is better for creating a good acid/alkaline balance in the body.Personally I take both in a smoothie.
I have heard of people promoting blue green algae as a meal replacement but it is important to note that it does not contain everything the body needs, no natural supplement does, most notably algae contains no Vitamin C.