I beg to disagree that the nature or essence of currency is consensus, at least not until Bitcoin came. It may be so in a small and primitive community but it cannot be in an advanced and large society.
The fiat currency is made up of a lot of policies, decisions, changes, impositions, etc which are not out of consensus. Of course it could be argued that it is hard to gather the opinions and ideas of everybody and that the very reason why there is a government is that it would act and decide on behalf of the larger population.
However, this is not really the case about fiat. The decisions of the few persons who decide about the direction of the currency are not really reflective of the people's voices and sentiment. So everything is merely imposed on the citizenry whether they like or not.
a medium of exchange can be anything. .. giving vodka to a friend for helping you mend a car.
a currency is more broader. within a community or nation.
a fiat currency is a government currency set by policy and law
as for the value. its not just a community consensus.
EG a rich person values currency differently than a poor person based on value and values.
but the underlying bottomline value normally has some bases on how much it cost to obtain and how much effort cost to pass on.
you can spot differences in values. in fiat.
take the policy law value.. minimum wage. where government in america thought $7.50 was worth 1 hours labour.
but the nation of america think $15 is worth an hour.
as for bitcoin.
in chaina/iceland. they feel thats ~$25k is worth 1 btc. however in germany. its more like $50k
this is why you see different area's have different values(philosophy) china will always mine cheap and value is less and always profit. so always mine. so when price is $45k they see it as OVER VALUE
where as germany cant afford to mine it so will see that when the price right now is below $50k will see btc as great value to buy.