The metallic dyes (along with pure white, jet black and pastel colours) are 'rare' dyes, that are just extra special shades - the metallic ones especially are...metallic so they make clothes look fancier if you dye them in those colours. As Frizze mentioned above though, there are actually two different types of those dyes - the 'normal' version which is unique and untradeable, and cannot be sold on the Market Board or traded to another player (and thus these are the ones you get on the Mogstation), and 'General Purpose' which do not have those restrictions, thus they can be bought and sold on the Market Board (these are crafted by an ALC with sufficient skill and materials or found through Retainer Ventures).

Either have the same effect when used though, they just turn your armour or clothing fancier colours. Incidentally on the dye interface the metallic dyes are listed separately to the regular colours, they're found at the right hand end by clicking the circle which is in multiple colours.