It’s hard to answer that without actually seeing a modern gift economy in action. Luckily, modern gift economies actually do exist. On a small scale, they exist among friends, who might lend each other a vacuum or a cup of flour. There’s even an example of a gift economy on a much larger scale, albeit one that’s not always in operation: The Rainbow Gathering, an annual festival in which about 10,000 people gather for a month in the woods (it rotates among various national forests around the country each year) and agree not to bring any money. Groups of attendees set up “kitchens,” in which they prepare and serve food for thousands of people every day, all for free. Classical economists might guess that people would take advantage of such a system, but, sure enough, everyone is fed, and the people who don’t cook play music, set up trails, teach classes, gather firewood, and perform in plays, among other things.
Corporate barter focuses on larger transactions, which is different from a traditional, retail oriented barter exchange. Corporate barter exchanges typically use media and advertising as leverage for their larger transactions. It entails the use of a currency unit called a "trade-credit". The trade-credit must not only be known and guaranteed, but also be valued in an amount the media and advertising could have been purchased for had the "client" bought it themselves (contract to eliminate ambiguity and risk).
Barter is a system of exchange by which goods or services are directly exchanged for other goods or services without using a medium of exchange, such as money. It is distinguishable from gift economies in that the reciprocal exchange is immediate and not delayed in time. It is usually bilateral, but may be multilateral (i.e., mediated through barter organizations) and usually exists parallel to monetary systems in most developed countries, though to a very limited extent. Barter usually replaces money as the method of exchange in times of monetary crisis, such as when the currency may be either unstable (e.g., hyperinflation or deflationary spiral) or simply unavailable for conducting commerce.
Trade did occur in non-monetary societies, but not among fellow villagers. Instead, it was used almost exclusively with strangers, or even enemies, where it was often accompanied by complex rituals involving trade, dance, feasting, mock fighting, or sex—and sometimes all of them intertwined. Take the indigenous Gunwinggu people of Australia, as observed by the anthropologist Ronald Berndt in the 1940s: