The money supply isn't the currency's value. Of course it is a factor in what traders are willing to pay to acquire it...but weather can be as well. Do you conflate the trade balance with the value of a currency too?
Market cap is money supply * last trade price. It mathematically can't be analog to money supply, any more than density can be analog to mass.
As in take the outstanding money supply and convert it, at prevailing rates, to U.S. dollars and look at that statistic over time. It’s a crappy metric, but it is useful in limited situations, e.g. when pricing rate or FX swaps.
Both market cap and money supply are metrics that sum across the set. In America we can just count dollars, because our unit of account is our currency. For countries with FX sensitivities, however, that sum is less meaningful in domestic currency than as a hard currency value.
Market cap is money supply * last trade price. It mathematically can't be analog to money supply, any more than density can be analog to mass.