To demand payment in specie, is to demand that which is specified.
So, just actually getting your dollar from the bank, rather than keeping a promise of a dollar from the bank. Doesn't seem much different today, right? But it might tomorrow.
In the days of the gold standards, a dollar was defined as a coin with certain specifications — including a specific quantity of fine gold. The problem inevitably arose, under these various forms of gold standard, where enough people demanded what had been specified, the banks were unable to deliver it to all of them as promised. This was inevitable, because money is not gold… money is credit.
People take out credit for all manner of things, with no regard or connection to the availability of gold to physically make all that money into coins for all the Negative Nancies out there who suddenly decide… Hey, wait a minute! I don't trust the bank's promises any more!!
Fortunately, today the dollar (or any other currency) is not specified as something physical that can be demanded — except for demanding a physical piece of paper with 'dollar' written on it from the bank, which you can hand to someone for their goods, instead of paying with your bank debit card or cheque, and they can pass on to someone else in the same way if they wish, or just pay it back into a bank again. Ultimately, it ends up either under a mattress or back inside the banking system… since it's useless for much else besides perhaps lighting a cigar, or wrapping a piece of used chewing gum before you can get to a waste receptacle.
TARGET2 is a system of bank clearing across borders within the Eurozone, where National Central Banks (NCBs) intermediate.
It would not be all that much different if the banks of Europe all directly engaged each other… except… these commercial banks don't both have an account in the same NCB's book, so recording a transaction in there is impossible. TARGET2 is accounting at the next level up in the hierarchy of the monetary system.
In this respect, TARGET2 at the ECB serves a similar purpose to the clearing system of the Federal Reserve Banks in the US, where each Eurozone nation (and its local NCB) is to some extent analogous to the regional Banks of the Federal Reserve system. A bank domiciled in the San Francisco Fed's region has an account at the San Francisco Fed. A bank domiciled in the New York Fed's region has an account at the New York Fed. Any transfers between these two banks are executed by clearing at the Federal level (in aggregate, along with all other transactions), not within the books of just one of the local Fed member banks.
Similarly, any transfers between a bank domiciled in the Eurozone and one domiciled in the US will clear at the next level up in the hierarchy - via the accounts of the two Central Banks (ECB and Fed) at the Bank for International Settlements (BIS). This is the top level of the global monetary system hierarchy. Unless we start trading with aliens, that is probably all we will ever need right?
So we have:
BIS
Central Banks (ECB, Fed, BoE, BoJ, PBoC, etc, etc)
In the Federated systems, US Fed & ECB, regional/national CBs present an additional layer
Then you have the commercial banks
Then you finally have the accounts of individual businesses and individuals
Your monetary transaction will show up at whatever is the lowest level, that there is commonality between you and your fellow transactor. If you are both within the US but in different regions, it will go up to the Federal level. If you are both in the Eurozone but in different countries, it will again go up to the Federal level.
TARGET2 is just the system within the Federated ECB level, where the account credit/debit balances of the various member Central Banks of the Eurozone are recorded.
Contrary to how it may have seemed, the world didn't love a dollar.
The world gave the illusion of loving a dollar, by storing up "promises of more dollars later". But the dollars themselves? No, they were largely sent right back where they came from — the US Treasury department — in exchange for an investment product that would return those same dollars, plus a few extras along the way in interest (AKA "US Treasury bonds" — "more dollars, later"). The US Treasury then got to spend the returned dollars over and over and over again, as the world just kept on sending them back in exchange for more promises. So that is how it famously came to be that "deficits didn't matter". They didn't, just as long as nobody stopped and considered the future.
So with this perspective, we can readily see that the world didn't assemble a trillions-of-dollars warchest of US dollars, because they just love a dollar, but they got rid of trillions of dollars because they didn't really want them after all. They wanted to "be able to say they had trillions of dollars", only because this gave credibility to their own currencies, and to grow their own economies. But aside from these bragging rights to "a massive stack of dollars that are due to them some day", they had no real use. It's not like the US would simply allow the rest of the world to buy up everything in the good old US of A and we'd own it all lock stock and barrel, in exchange for all these dollars we have that, on paper, say we could buy it all many times over now, is it? It's clear that is not allowed — America buys up the rest of the world, not the other way around! Anyway, I digress... Let's get back to the world and it's love for a dollar...
Today (since 2007 when the global financial crisis started to erupt) the problem is that the world actually has fallen out of love with the idea of "more dollars later". There was a realisation that there were fewer than a Trillion dollars in existence in 2007 (the US monetary base) and many, many times that amount was already owed to people all over the world in many different ways and from many different entities, but not least by the US Treasury department. The world appears to have stopped investing in the future of the US economy and long term debt investment products, and has instead switched to demanding actual dollars or very short term Treasury investment products, such as 13-week Treasury bills (when the "yield" on a bond goes down, this means the price has gone up - i.e.: that there is great demand to buy them... As we can see, at the moment there is insatiable demand for 3 month Treasury bills; which are "as close to cash as you can get without physically stuffing it into a shoebox under your bed"... which is not something that the world's national Central Banks are in the habit of doing of course).
The world finally does actually love a dollar, rather than a long term debt asset that promises more dollars later. It turns out, the world loving the dollar isn't such a good thing for America ... or any of the other countries that have built up massive levels of debt in the good times of the past. They can't pay all the debts with the amount of base money available within the system today. So, do you think there might be only one realistic way to pay all these debts, without the system collapsing and probable breakout of another world war?
Ooops!
Perhaps it would be better to ask where all the love came from and then left?