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 Fiat: issuance centralized, arbitrary, and unpredictable (also not private if digital)

Monero: issuance decentralized, requires PoW, and predictable

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Exact opposites 
 Actually Fiat is Money by decree.

All the other adjectives that you added are properties of government fiat, but don't define fiat.

Monero is Fiat since it has no intrinsic value and it became money by deceleration.
All the other adjectives that you added are indeed properties of Monero, but don't make it any less Fiat. 
 Fiat is an authoritative order or command

No one is commanding or ordering anyone to make Monero money. It's all voluntary and emergent so I'm still not following what you're saying. 
 Actually Monero was an authoritive order. The creator of Monero (whomever that be) said "let this be the genesis block!". He did not have power to force his order to be accepted, so he used other means to make his order accepted. 
 I think I see what you're saying now. But when people are normally talking about fiat in this space this is not what they mean. They're talking about government issued legal tender. 
 I know.
It's important to point out that this way of thinking is wrong to insure people understand that Blockchain is not a full fix for gov. issued currency. Since they are both Fiat the share a lot of defects 
 I think the major difference (in addition to everything I first listed) is governments have a captive populace and can force acceptance of their fiat. Monero/crypto devs can't force anyone to use it. And if enough users don't like what devs are doing it will be forked and take most of the network with them (You can't fork government fiat). This was Moneros origin story to begin with.