Is cognitive psychology similar to biological psychology?

No it's not. Cognitive psychology tries to study the constructs people create, the opinions and views they create about the world around them. People have different cognitive views on the world. Cognitive psychology states that the objective reality isn't that important, it's the subjective views that people create to understand the world and live in it.

Biological psychology studies the inner workings of the brain (so how neurons work, how the memory works, how the brains causes the actions we make...). That's more of an exact science instead of theories.