I am trying to understand the definition of money as you have worded it. Why people would choose to accept one over another does not matter for defining the term. In some places, both the USD and the EU are accepted as a medium of exchange as well as perhaps a local currency. Am I correct in understanding that only one of these can be considered money while the others cannot?
Assuming pure global anarchy in which nails and screws are both commonly used as a medium of exchange, would nails be considered money and screws not if nails were used in 51% of transactions and screws in 49%?
Any country in which two currencies are widely accepted. I will admit, I am not familiar enough with current world politics to know of many good examples but it is my understanding that Somalia widely accepts the USD as well as their own currency.