[Floordford]

Exhaust Manifold- the stock, cast metal exhaust component that channels exhaust gas from the engine into the exhaust system.
Exhaust Header- the aftermarket tubular exhaust component that channels exhaust gas from the engine into the exhaust system. Made in different configurations. Long tube style, shorty style which is usually a direct stock replacement, mid length style.

Basically a manifold is stock and a header is aftermarket.