These are two of the three major perspectives on sociology. Each of them understands society and social phenomena in a very different way. Functionalism looks at the large structures in our society while symbolic interactionism looks at the way in which individuals act within the society.
According to the functionalist perspective, everything in a society has a role that is necessary for the functioning of the society. This means that even poverty and economic inequality, for example, play an important role in keeping our society stable.
Symbolic interactionism does not ask about such "big picture" questions as why poverty persists. Instead, it looks at how individuals act. It says that people attach meanings to various things that they see as symbols in our society. They then act in ways that accord with the meaning that they attribute to those symbols. For example, one person might see sagging jeans as a symbol of poverty and avoid or be suspicious of a person wearing them. Another person might react to that symbol in a different way.
Functionalism considers society at the structural, or "macro" level, focusing on the roles that institutions and even behaviors play in the workings of society. According to functionalist thinking, all parts of society are connected, and institutions have functions within this organic whole. For example, sociologist Emile Durkheim, one of the founders and earliest proponents of what would become known as "functionalism," argued that religion served a societal purpose: it encouraged people to adhere and accept social norms that contributed to order. Symbolic interaction focuses on the interpersonal, what we might call the "micro" level of society. In particular, it looks at the meanings people give to their interactions with others. Even behavior, symbolic interactionists argue, is symbolic. People, as the first answer indicates, interpret behaviors in different ways, and they behave in ways that are shaped by these responses. They are not as interested in the functions that behaviors or human actions play in society as a whole as much as the ways in which individuals' interactions with each other are shaped by symbolic interpretation. Because this process is subjective (it depends on individual interactions) it is less deterministic than a functionalist perspective. Using the example of religion again, a symbolic interactionist perspective would look at the meanings people attach to religious symbols, which broadly include the religious actions of individuals in society and religious leaders.
With regard to social interaction, the symbolic interaction theory asserts that symbols are at the heart of human interaction. Accordingly, an individual’s responses and behavior are subsequently directed by their interpretation of the symbol in question. Their interpretation of the symbol is influenced by their social interactions with other members of the society that hold different interpretations of symbols. It is important to note that symbols do not have meaning by themselves and that the meaning assigned to a symbol by a person is a result of their interaction with various other people. These interactions then guide their subjective interpretation of the symbol and influence their response.
On the other hand, the functionalist theory proposes that all elements in a society are interdependent. Each element plays its own unique role but is dependent on others and this dependence ensures the society functions optimally as one unit. The society is connected by social consensus where there is an agreed-upon set of guidelines that govern interactions for the good of the entire society.
One major difference between Functionalism and Symbolic Interaction (SI) is SI is a Micro Theory (small picture) and Functionalism is a macro theory (big picture). One great example of SI is Jerry Seinfeld's form of Comedy. I attached a link for the Close Talker bit from Seinfeld. It basically is the epitome of Symbolic Interaction.