Hello Rokr,
You got the definition of the 2 words above.
Some examples to show the difference:
"Do you like this song?"
"Indeed, I do."
You are confirming without doubt, that you like it.
" Is this the song you told me about?"
"Exactly. It is the one."
Here you affirm precisely.
In the first example you can't use "exactly " instead of "indeed" ,
you can't say " Exactly ,I do ".
However in the second example you can use "indeed" as well. It won't be a synonym, but it is possibly used.
"Indeed, it is the one."
Here you say ,"it is the one without doubt",while using "exactly" means," it is precisely the one."