What is the difference between eluvium and alluvium?
Both are very similar, as they are based on minerals undergoing erosion and the presence of water in the erosion and deposition cycles, the difference is quite subtle, an example is defined in the Gold Prospecting in Western Australia website Alluvial Gold and Eluvial Gold as being

Alluvial deposits are mixed with other deposits and are washed downstream in rivers or transported in among other sediments with water as its medium. An example is that gold deposits this way are smoothed and are ground down the further from the source.

Eluvium deposits are in situ or very near its source, rather than been washed away by water.  For example, eluvial gold are often large nuggets nearer to its source.

A much more succinct definition is provided by the Australian Museum:

Alluvium:


  Detrital material which is transported by a river and usually deposited along the river's pathway, either in the riverbed itself or on its floodplain.


Eluvial:


  Weathered material still at or near its point of formation.