Algae, or singular: alga, are a group of simple, typically autotrophic organisms, ranging from unicellular to multicellular forms. Seaweed and fresh water moss are types of algae.
Algae belong to the Eukaryota domain and the Protista kingdom.
Fungi are a group of unicellular or multinucleate organisms that live and grow on decomposed matter. Mushrooms, yeast, truffles are types of fungi.
They are also a member of the Eukaryota domain, while belong to the Fungi kingdom.
Algae and Fungi are most commonly associated with moss and mushrooms. The green slimy things that are found in lakes and in unclean aquariums are known as Algea, while Fungi are the fuzzy things that are found on spoilt food, or mushrooms. Though, both may look similar, both are different compared to each other.