The structures and functions of the two are different.
Both are extracted from red algae plants (usually Gelidium), and agarose is used to produce gel products. For example, the electrophoresis gel we make. Agar, also known as frozen powder, is used as a bacterial culture medium, food gelling agent and slurry in the textile industry.
In terms of structure, agar is composed of agarose and agaropectin. Agarose is a linear polymer whose basic structure is 1,3-linked β-D-galactofuranose and 1,4-linked 3,6-anhydroα-L-galactofuranose. Agar pectin is a heterogeneous mixture of many smaller molecules. Their structures are similar, but they contain sulfate and carboxyl components and have poor gelling ability.