To be "functional" is to be flexible and strong enough to be able to perform the (any) task at hand.
"fitness", is best described ( to me) as being able to perform that task, and the ability to recover as quick as possible to be able to repeat the task.
"Exercise"?
Like all exercises, wanting to get better at squatting requires, squatting and in a progressive manner.
Done well, the byproducts are being stronger (flexible) and healthier, this is just one small aspect of improving function.
for a football player skills work is key.