Algae are classified according to their

color of pigment
type of locomotion
type of reproduction
growth patterns

Algae are classified according to their color of pigment.
There are many different types of algae, which aren't necessarily related to each other and the most obvious distinction between them is their color. So we have Chlorophyta and Charophyta, which are green algae; Rhodophyta, which are red algae; Phaeophyceae, which are brown; Chrysophyceae, which are golden, etc.

Digestion because it removes waste