The answer to this question is that while many people have historically viewed behavior analysis as a branch of psychology, the two disciplines take fundamentally different and antithetical perspectives to account for variability in human behavior.
In general, Behavior Analysis does not concern itself with mental states or inner thoughts when it comes to describing why we behave the way we do. Rather than focusing on “the mind,” behavior analysts look at behaviors, or in other words, what we do, as a consequence of things that happened previously. Simply put, we will repeat things when the consequences are pleasant and we will stop doing things when the consequences are unpleasant. Behavior analysis, as it suggests, focuses on treating behavioral problems from a purely behavioral perspective/lens. Functional analysis, gathering of data to establish trends, and then a subsequent intervention program or plan that utilizes various forms of operant learning are then applied.
Psychology focuses on the mind. Psychology as a discipline largely hypothesizes internal explanations (personality traits, mediating forces and other structures in the brain, etc.) explain differences in human behavior. Psychology looks to explain behavioral variability by appealing to internal causes that are typically seen as inside the mind (e.g., mood states, personality traits, hypothesized structures such as ego and/or drive states)
In short, the difference can be stated as follows: In the ENVIRONMENT (Behavior Analysis) versus inside the MIND (Psychology).