Money seems to be about gold but banks about silver. Is this due to an evolution of the status of the valuable metals themselves? Is it a complicated (e.g. ateji) etymology?
Firstly, the native word 金（かね） in お金 only means metal and not gold. You may have mixed it up with the Sino-Japanese 金（きん） that means gold (it also means metal as a morpheme, but not for a standalone word). The native word for gold is こがね "yellow-metal". Thus money is called お金 just because coins are made of metals. No mystery :)
On the other hand, 銀行 is a relatively newly imported word from Chinese originally means 銀 "silver" + 行 "guild". What was traditionally the standard money in Japan is a quite debatable topic (gold, silver, copper, or rice??), but China has a long tradition of silver standard system, so that's why silver is the synonym of money for them.