If take a look at the Wikipedia article @Fizz provided in the comments, it does say that Functionalism is different to Behaviourism
because it is only concerned with the effective functions of the brain, through its organization or its "software programs".
The full explanation of why it is different is that Behaviourism is
a systematic approach to understanding the behavior of humans and other animals. It assumes that all behaviors are either reflexes produced by a response to certain stimuli in the environment, or a consequence of that individual's history, including especially reinforcement and punishment, together with the individual's current motivational state and controlling stimuli.
In other words it looks at how people's current and past experiences affect the person's mood and behaviours.
Functionalism states that
mental states (beliefs, desires, being in pain, etc.) are constituted solely by their functional role – that is, they have causal relations to other mental states, numerous sensory inputs, and behavioral outputs.
Comparing the human brain to the computer whilst trying to explain this philosophy, the Wikipedia article points out that
brains are physical devices with neural substrate that perform computations on inputs which produce behaviors.
Where Behaviourism just looks at the initial stimuli and resulting behaviours, Functionalism looks at the brain functions and tries to explain how behaviours manifest themselves in reaction to the information the brain receives.