LedgerLoops is a set of peer-to-peer protocols for Collaborative Finance, which can be used to support multiple economic arrangements. Here are some loose definitions of some of them (under construction). See also Constructing systems of exchange (PDF) by Matthew Slater for some more precise definitions.
A single transaction in time, exchanging only goods or services and not currency or credit. Due to the rareness of Coincidence of wants it is rarely used in practice by itself, but it can be combined with in-kind lending.
When two parts of a transaction cancel each other out, but they don't coincide in time.
Agreeing to cancel out a set of otherwise unrelated credits against each other.
Apart from barter, barter+lending, and barter+lending+netting, there are a number of other ways to complete a transaction of goods or services, that we would generally refer to as a payment:
The mechanics of the transaction work as if the currency were a (commodity) good exchanged in barter, but the asset changing owners is not something the recipient actually wants to use.
The commodity used as currency may be direct ownership of a physical good like gold, or commoditized credit, or (e.g. for collateral-backed credit) something in between.
The administration of ownership might be through physical possession (for instance a piece of gold, coin, or bank note changing hands), or through a (system of) ledger(s) as is the case in bank transfers and crypto-currency payments.
We often think of bank transfers and cash payments as practically equivalent, and (even though banks can fail) we often think of money as a commodity good you can own.
Think exchange of bearer IOUs from a named party (whether physical bearer notes or on a ledger) rather than generic bank notes, e.g. paying with a voucher.
Payment through netting can be modeled as an exchange of a named credit, while performing netting on the resulting credit balances in the same transaction. This is a core concept used for multi-hop payments in systems like Ripple Classic and Interledger.
Structuring different transferable credits into a named collection, to remove some of the stochastics (generally profitable but destructive, since it makes the resulting bundle hard to value accurately).
Exchanging one currency or named credit against another (no goods or services involved).
Participating in currency exchange with the sole goal of making a profit.