functionality = any or all of the operations performed by a piece of equipment or a software program
My computer has a high level of functionality. It can do many things.
function = the way in which something works or operates, or the process of operation
My computer has many functions.
In the above examples you could say they have the same meaning. However, when you start to use the words in a different context, you have to use one over the other. Example:
Identity is formed in early childhood and the strength and functionality of family relationships play a huge role in its development and outcome.
It might be helpful if you could give us the context.