I was recently reading through a textbook and was unable to clearly identify the differences between the two due to a vague definition of both. Can someone provide an in-depth explanation of the two and perhaps provide examples?
Behaviorism is the idea that psychology should be limited to what it can directly observe: behavior and the stimuli that drive behavior. A behaviorist approach to studying a psychological phenomenon would be based on studying observable behaviors and the observable things that cause those behaviors. Behaviorist explanations of the phenomenon would not rely on descriptions of internal processes, like thinking, since those are not directly observable.
Biological psychology takes the perspective that pyschological processes (e.g. thinking) are rooted in biology, and focuses on how biological processes cause and interact with psychological processes. Techniques like measuring neural activity through EEG or fMRI are common, as are (non-human animal) studies that involve more invasive manipulation of neural tissues. A biological psychology approach to studying a psychological phenomenon might identify particular patterns of brain activity that are related to the phenomenon, genetic correlates, or neural mechanisms that give rise to the phenomenon.