they do pretty much the same job but dont look the same.. manifolds are cut from a block of metal or they are made from melted metal and they are much thicker while headers are made from bent and welded steel/stainless steel thin but strong piping.
From what i've seen headers are good for natural aspiration engines. Headers can be also used for boosted engines but the piping is thicker. Manifolds are used for many stock applications or low turboed vehicles. Manifolds tend to run quieter since the walls are thicker also they are faster and cheaper to make.
Headers
manifold