Okay, this is a nice morning, and I'm feeling inspired, so I'll bite

The most wholesome form of money, in the eyes of the SINners, is a bank account registered to your name. It contains Nuyen and/or Scrip. It's accessed through your commlink (somewhat insecure, not recommended), through a named-credstick attached to your commlink (you have to approve all transactions by physically pressing a button on the practically unhackable credstick) which is more secure, or it's accessed through a stationary (home or office) terminal (also fairly secure).
Nuyen is a universal currency; it's accepted in most parts of the world, SINing and SINless, because everyone knows that it'll be accepted from them in turn. Also, the Nuyen is completely electronic; there's no Nuyen bills. Some (corporate) territories may not recognize Nuyen as legal tender, insisting on Scrip, but Nuyen still accepted on the black market.
There are no unique individual Nuyen; bank accounts simply have a balance in Nuyen, and only high-level banks can issue new Nuyen, all under the supervision of Z-OG. (Lower end banks are still allowed to have Nuyen accounts, but are not money-creating banks.) Z-OG regularly (perhaps hourly, or even faster) checks the balance of all banks allowed to run Nuyen accounts, to see if irregularities have occurred. If irregularities occur, a team of Swiss Accountant Ninjas descends to check the books and rectify the discrepancy. Nobody wants to be on the receiving end of
that.
Corporations can issue Scrip as legal tender inside their jurisdiction. It's often illegal to spend Scrip outside the corporation's jurisdiction, making sure the money stays inside the corporation's little mercantilist universe. Exchanging Scrip for Nuyen or other outside currencies may or may not be legal; if it's legal it's probably still pricey, since corporations want to discourage their citizens from buying stuff outside that the corporation can provide itself. Some corporations may issue cash Scrip, others think that's dated.
Nation-states issue their own currency, which is a little bit freer than Scrip; generally you're free to exchange it for Nuyen or spend it out of the country, although there are exceptions. Most nation-states are bound by the Business Recognition Accords to recognize Nuyen as legal tender alongside their own currency however.
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Cash: some nation-states and corporations issue cash. Cash is tricky because protecting it from forgery tends to cost more than the bills are worth (nanomanufacture!). This results in cash basically being like jewelry: it's production, not just the raw materials, add to the value. Even well-forged cash (with all the requisite nano-level watermarks) represents a significant investment in production, and therefore value. It's kind of like having a Black Mint alongside the Fed, but since it's in the Black Mint's interest not to cause rampant inflation, the system works. (If someone clever sets up a second Black Mint and floods the country with cash, a shadowrun/terrorist strike will happen in record time.)
Cash is still important, because of the significant SINless population. A lot of them don't want to use Matrix money too much for fear of attracting significant attention from Big Brother, and the anonymity of Cash helps. It's also safer from hackers, which matters a lot to people who can't afford secure commlinks. Cash is also popular with SINners who like to slum; to buy drugs with for example. If a wageslave is discovered to possess a lot of cash, it won't look good on his Performance Review.
Credsticks: really simple machines, but because of that, very hard to compromise. They carry a One-Time Pad, and are connected to a single bank account which also has that OTP. The OTP is big enough to never run out, and (mathematically proven) an impossible to break encryption method, used to communicate securely.
The credstick can do two things: view the balance of the bank account, and transfer money to another account. The money isn't on the credstick but in the bank. The credstick can't do anything else, so even if you hack it, the only thing you can do is empty the bank account, not add to it. However, since the credstick doesn't need any remote functionality, it's built so that remote logging in (and hacking) isn't possible; you need hardware access for that.
Credsticks may be linked to an anonymous account or to an account registered to a specific person. In the latter case, that person can revoke the credstick (if stolen, perhaps), and place limits on how it may be used (whitelist, transaction limit, etc.), similar to an advanced bank card. Anonymous accounts don't have these options; if the stick is lost, the finder gets the money. If not found, then free money for the bank.
Why do corporations allow anonymous credsticks? First, a surprising amount of money is earned by credsticks getting lost. Second, because it enables the SINless to participate in the economy and buy products, which is good for business. Third, because it facilitates a corporation's illegal dealings.
Who uses credsticks? Everyone. SINners use named credsticks as a security feature; even if their commlink is remotely hacked, you still need to physically press a button to authorize transactions. These credsticks fit into commlinks like a mouse into a computer: completely commonplace.
Anonymous credsticks are used for things you don't want your wife or boss to know about. Kind of like prepaid phones. And they're used by the SINless to engage in more expensive purchases.
As you might have noticed, SINless are basically allowed to engage in the economy by the corporations, as long as they have money. This makes sense; just because you've deprived them of civil rights and social security, is no reason not to let them buy your soyburgers.
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Other Currency, Barter: despite the availability of Cash and Credsticks, the SINners are on the short end of the stick in the realm of financial instruments. Money is a very useful tool for structuring barter, and making it possible to trade things of unequal value. However, not every currency is equally useful. In blighted Puyallup, Matrix access is scarce which lowers demand for Nuyen and raises demand for Cash, for example. There are regional differences, and a clever hustler can make a living as a moneychanger. Besides that, there are all sorts of communes of weirdos, who have unusual capital (like telesma) for trade. Many of those can function as currency, if they're hard enough to falsify and rare and valuable enough.
Credit: if an area has a shortage of currency while goods are still traded or bartered, eventually there will pop up some system of credit; like the local store recording that you still owe them ten Nuyen, while they owe the baker five and the butcher four, and so forth. This requires some trust between people, but if that's possible then this system can function fairly well. Again, someone can make a living by being a credit-trader who can vouch for people's trustworthiness if they want to do business but don't know each other well enough. Or by negotiating the value of one type of money used to settle debts in another kind. Even the Barrens have their bankers.
Actually, the Banker of the Barrens could be an interesting NPC.