Both do almost the same thing by expelling the exhaust gases from the engine. Except the headers expel it into the exhaust system directly, while the exhaust manifold on a turbo car expels it to the turbo, to run the turbo.

Also the material used to make each one is also critical. Headers can be mild or stainless steel, while tubo manifolds can be cast iron/steel, stainless steel or thick gauge mild steel (steam pipe). Turbo manifolds are never thin gauge mild steel like what you get in a header or other exhaust components...the weight of the turbo hanging off it is too much for the thin stuff and you will end up cracking the manifold in no time.