Metal is the phase of the Wu Xing with no counterpart at all in the Greek four, and comparing the two schemes at that point is the quickest way to see that they are not versions of one another.
Its content comes from its place in two cycles. In the generating cycle, sheng, Earth produces Metal and Metal produces Water, the second step usually explained by the condensation that forms on a cold metal surface. In the overcoming cycle, ke, Fire restrains Metal, since fire melts it, and Metal restrains Wood, since an axe fells a tree. Those four relations are the phase. A list of things associated with metal is downstream of them.
In the classical Chinese medical literature Metal is the phase of the lung and the large intestine, of the skin and body hair, of autumn, of the west, of the colour white, of the pungent flavour and of grief among the emotions. Those are correspondences recorded within that system, set down here as description and not as guidance of any kind.
The word itself, jin, means metal in general and gold in particular, and the phase covers the whole class rather than a single substance. Its season is autumn and its work is contraction, gathering in, cutting away what is not to be carried through the winter. Where a Western source glosses Metal as air, which happens often in popular writing, the gloss is an attempt to force five phases into four elements and it should be discounted.
Sources Science and Civilisation in China, Volume 2: History of Scientific ThoughtJoseph Needham with Huangdi Neijing (The Yellow Emperor's Inner Classic)Traditionally attributed to Huangdi; actual authorship unknown