(I do not know if this is an answer but having read OP's profile, he seems to be trying to get with the program of SE, so I will try to help.)
First, the answer to this is more convoluted than it seems at first sight. Hence, it does require more elaboration from OP, such as narrowing the question, or at least establishing some terms of reference in the question.
Second, unless one is well-versed in not just history, but also economic theory and jurisprudence, the answer will most likely be unsatisfactory.
Allow me to illustrate with a few points:
- concept of currency
- concept of barter
- private property
Concept of Currency
- In Wealth of Nations, Adam Smith used corn, silk and other commodities as reference for currency because (and this is where it gets tricky), he was trying to show the nominal value of goods (think inflation), regardless of effort (labour) required. In his chapter on Division of Labour, paragrph 4:
In agriculture, the labour of the rich country is not always much more productive than that of the poor; or, at least, it is never so much more productive as it commonly is in manufactures. The corn of the rich country, therefore, will not always, in the same degree of goodness, come cheaper to market than that of the poor. The corn of Poland, in the same degree of goodness, is as cheap as that of France, notwithstanding the superior opulence and improvement of the latter country. The corn of France is, in the corn provinces, fully as good, and in most years nearly about the same price with the corn of England, though, in opulence and improvement, France is perhaps inferior to England. The corn-lands of England, however, are better cultivated than those of France, and the corn-lands of France are said to be much better cultivated than those of Poland. But though the poor country, notwithstanding the inferiority of its cultivation, can, in some measure, rival the rich in the cheapness and goodness of its corn, it can pretend to no such competition in its manufactures; at least if those manufactures suit the soil, climate, and situation of the rich country. The silks of France are better and cheaper than those of England, because the silk manufacture, at least under the present high duties upon the importation of raw silk, does not so well suit the climate of England as that of France. But the hardware and the coarse woollens of England are beyond all comparison superior to those of France, and much cheaper too in the same degree of goodness. In Poland there are said to be scarce any manufactures of any kind, a few of those coarser household manufactures excepted, without which no country can well subsist.
What I believe OP is looking for, is not really definitions of fiat currency/money, but understanding how societies functioned before the invention of fiat money. Hence, the alternate system of barter in the question title.
Concept of Barter
In the context of this question, bartering is seen as an accepted form of exchange for goods and services without the use of fiat money. To this end, it is a natural choice if money was not available (not yet invented, for instance). Unfortunately, on a deeper level of analysis, this is not true.
The mainstream economists' view that barter should be seen as a `natural' phenomenon of human nature and as the origin of money is rejected. Barter occurs in specific socio-economic conditions which may obtain also in economies which know money. When there is a very low supply of currency, money may cease to function as an index of value for all goods and itself become an item bartered. This is likely to occur when small discrete social groups wish to maintain autonomy. Unlike money payment, which requires a further transaction before value is realised, barter satisfies demand immediately and is of its nature discontinuous. As with car trade-ins in our economy barter occurs when people cannot afford to keep money, and it becomes a system when society is atomised to the extent that people do not exploit the variations in exchange ratios between different communities. Using the case of the Lhomi of north-east Nepal, it is shown that althoug the exchange of common produce, as opposed to rare valuables, is most likely to approximate to a notional 'equilibrium price', the practice of barter with no established measures of weight and volume means that there can be no underlying index of value/numeraire. Each transaction exists virtually on its own. Thus, although barter is an egalitarian mode, it contains no protection against changing exchange ratios which may harm one partner. Barter tends to take place between people who know one another, because it is only by the establishment of customary times and places for exchange that the costs of searching for partners, waiting etc. are avoided. Delayed barter, which often occurs with valuables, requires non-economic means of ensuring repayment, but the ritualised trade-partnerships which the Lhomi employ are self-limiting: restricted relations cut traders off from the wide, unpredictable world of the capitalist end sale. Business often fails and the traders suffer.
Source: Caroline Humphrey, Barter and Economic Disintegration, Man, New Series, Vol. 20, No. 1 (Mar., 1985), pp. 48-72, Royal Anthropological Institute of Great Britain and Ireland.
Again, back to OP's intent in the question, I believe what OP meant to research on is not just how societies functioned without fiat money, but also how they were compensated (e.g. for their effort). This begs the next question, what if these societies did not understand (hence, did not practice) the concept of private property?
In economic history, private property is considered crucial to the development of modern economic society (and the Industrial Revolution). Conveniently, we can point to John Locke (1634 - 1704), as the one who helped us (modern society) identify the value of private property. So, how did the Romans, Assyrians, Mongols - (name your tribal culture) - get paid before Locke? Now we get into legal theory, what is private property?
What I hope to show, especially to OP (and anyone new to History SE), is the need for clarity in a question. In this sense, the somewhat strict requirements when posting questions is utilitarian, not an arbitrary after-thought.
Let me end by saying, I am well aware this post does not answer OP's question. What I hope to show is, the question itself is unanswerable in its current form (well, for me anyways). Much more thought and revision is required.