As promised: Introduction

What is money?

Money is a medium of exchange generally in the form of coins and banknotes and balances. That's basically what you use to buy your daily things. But money on a board game is not the same though it's still money it's not currency! Or should I say it's a currency for board game aficionados.
Also your marbles, your pugs, your collecting cards and even your candy, when you were younger probably was money
The money supply of a country consists of currency (banknotes and coins) and bank money (the balance held in checking accounts and savings accounts).
Nearly all contemporary money systems are based on fiat money (the US$ has been fiat money since 15 August 1971, when the United States unilaterally terminated convertibility of the US$ to gold brought, the Bretton Woods system to an end. Federal Reserve Notes are no longer backed by hard assets such as gold. Federal Reserve Notes are now backed solely by the government's declaration that such paper money is legal tender in the United States.).

What is a currency?

A currency is a generally accepted medium of exchange.

Most known currencies are US Dollar, British Pound, Euro, Yen, Swiss Franc have been backed and centrally governed by governments and institutions. 

This means that the central authorities governing this medium to facilitate exchange among their people agree to the value and a set of law to govern it and they call that medium a currency.

You hear a lot about fiat currencies

Currencies can be influenced by forces like government policies, and economic instabilities.
You can see the influences in  today's main currencies variations when:

1. Foreign policy changes affect either the expenses of a country, the way the country is perceived internationally, or a commitment to a situation.
2. National policy change
3. The central bank affects the way their citizens, companies and government are incentivised to save or to spend their money. (Ie: interest rates, local consumption, etc) 

Overall economic performance which most often is correlated with the quality of education and trust in institutions

and trust in institutions

What is a digital economy?

A digital economy is pretty much what we have today, it's an electronic payment. It's when completing a transaction is as simple as clicking your mouse or swiping your card and confirming transaction. Banks have adopted the digital economy as it has cut a lot cost on paper and postage.
Since the 60s, electronic payments have been rapidly growing as payment by check and cash have declined as it has cut cost on transportation. Recently with the growth and dissemination of the internet, it has been proven that offering electronic payment can help improve customer retention for businesses. A customer is more likely to return to the same e-commerce site where his or her information has already been entered and stored.

Digital economy, is pretty much everything other than barter check and cash transactions.
Advantages:

• May be controlled by a set of defined parameters.
• Transactions are generally made:
• Cheap or free as moving funds around has a very little cost
• Simplicity is design and usage process, which today generally means as easy as a click.
• Do no need to store any physical goods
• Allows you to make billion dollar transaction with similar cost as a $5 transaction
• May be controlled by a set of defined parameters.
• It can be frauded at a distance
• Transaction may have a cost whereas cash is costless
• May not necessarily represent the reality of things
• It's not tangible
• May be distributed

Disadvantages:

• Double spending as it is digital has been a big problem for digital currencies. Bitcoin solved the double spending issue through global ledger (which will bring us to distributed economy)
• No tangible asset, rather it being gold as a base, it's an algorithm that fixes the unit base.
• System can theoretically be hacked
• If coins are stored online they may be hacked
• It is risky as it is still early in the adoption rate and there is no clear regulation as of yet.

What is a distributed economy?

It is a currency that is owned by nobody else than the market and the peer supply and demand.

It's closer to a bartering economy than the way we know it. Or should I say that it is more like our economy before Bretton Woods when people were trading gold or equivalent gold backed money as their currency.
It will generally not issued by any central authority, rendering it theoretically immune to government interference or manipulation
The main difference with gold, is that digitally distributed currencies can be programmed in a way that makes it more efficient than gold when trading, especially micro (transaction < $1) or macro (transaction > $100K) transactions!

Also as soon as you own a phone and have access to electricity, you can actively participate in the value of that economy.

What is a crypto-currency?

A crypto-currency is a currency that uses cryptography for security. It is difficult to counterfeit because of this security feature at its core.
Cryptocurrencies may offer pseudo-anonymous transactions which positions' them well for nefarious activities such as money laundering and tax evasion.

The first digitally distributed cryptocurrency to capture the public attention was Bitcoin, which was launched in 2009. Bitcoin's success has spawned a number of competing cryptocurrencies such as Litecoin, Namecoin and PPCoin.

All those cryptocurrencies use

They are 3 main reasons why bitcoin like crypto-currencies are more successful than any previous attempt to digital currencies:

1. They solve the double spending problem of digital currencies by adopting a global ledger, therefor, all transaction are in essence public on the network.
2. They are distributed, therefore they are worth as much as demand as supply, not as much as a the arbitrary authority like the central bank decides.
3. Anonymity, is at it's core. All transactions from one wallet address to another is public, but wallet holders are not necessarily authentified.