Really, they are not the same. The key is in how they are distributed.
When a crypto fork happens, everyone who holds one unit of the currency receives a unit of the new currency. The market cap of the original currency is split between the original and the new currency. No one is better off, and no one is worse off during a crypto split. Each coin can buy less than the original coin before the split, but the two coins together add up to the same value everyone had before the fork.
In contrast, when governments print money, people who hold the original currency NEVER receive a share of the money that gets printed. Invariably this money goes to banks and big corporations with government contracts. However the market cap still gets split between the existing currency and the new currency. The banks and corporations get first-mover advantage with the printed cash as devaluation of the original currency can't happen until it enters circulation. By the time the new money "trickles down" to the average citizen through wage inflation, everything already costs more. If the wage inflation happened immediately as prices rose, this would be a non-issue, but it doesn't. It always lags behind, and that is why those last to receive a share of the printed money are net losers when it comes to inflation.
Money != Wealth
Fiat money has a "market cap" too, but it's less about a number and more about the wealth of a nation. Wealth can't be created by printing money, it is only created via production and trade. In a very wealthy nation that is producing and trading a lot of things, a fiat currency will be representative of that economy and be worth quite a bit! If, for example, we quantify the production and trade of a nation so that 1 unit of production is worth 1 unit of the currency, you can easily see how printing more money doesn't make anyone more wealthy.
If the nation has an output of 1 million production and has 1 million units of the currency in circulation, everything is fine. If the government then prints another 1 million units of currency, there is STILL only 1 million units of production. Now each unit of the currency is only valued at 0.5 units of production. As a citizen, you would need 2 units of the currency to buy what you needed to buy before with 1 unit. If you get that unit right away (as in a crypto fork) then you are no better or worse off than before*. If someone else (like a bank or company) gets that money first, then as THEY use it, prices will rise for you first and for a period of time dictated by the "velocity of money" you will be paying higher prices for everything with only your original stake of currency to buy it with. You become poorer. By the time the wage inflation arrives your wealth has been eroded.
Hmm, good point.
To save Australia from the 2008/09 recession the government gave all residents $900 to go out and spend to help grow the economic spending, i am sure that money didn't come from some saving account, it would have all been printed.
As you can see from the above, printing and distributing money has no effect on the overall wealth of the nation. It just makes everyone's currency worth a little bit less. The only way to grow an economy and reduce poverty is to increase the production and trade the currency represents. By doing this, without printing money, you make each unit of currency worth MORE. That is how nations and the people in it become wealthy!
* You are actually a bit worse off than before because the government likely used the printed money to pay off debt with reduced-value currency. This means production with a real value of X units was settled for X/2 units of currency, essentially stealing value from the economy.