This discussion will develop as do more on particular financial markets.
The kinds of agents involved here will get very complex. In order to anchor this back to the real economy, I think it makes sense to start with something loosely called the 'firm' - by which I mean, an economic agent which produces actual stuff. This stuff is traded outside of the financial markets.
As well as firms, there are institutions which exist only to play roles in the financial markets. These we can call 'financial institutions.' Banks and insurers are common types of financial institutions. (These may also play roles in 'retail' finance / insurance providing services to individuals rather than firms. Won't go into that yet.)
But it is often more useful to identify financial agents by the roles they play rather than their corporate identity. Often institutions will play numerous roles, which can get confusing. Also, terms for different roles can vary, and even seem contradictory, depending on the market's set-up (eg. we may want to talk about buyers and sellers. But someone 'buying protection' against risk in a derivative trade is also 'selling exposure'.)
In general, the essential roles in a primary financial market are:
Investors (Lenders)- InvestmentFunds
Arrangers and middlemen - FinancialIntermediaries
Firms want to get their hands on financial capital - in the simple case, to buy production inputs. One way for them to do this is simply to exchange real stuff (eg. goods they have produced) for already-existing exchangeable instruments (securities or money) that they can spend. But, often, in order to get financial capital to spend now they will in fact create new financial capital. They do this by issuing new securities - contractual rights to or promises against their future income. In DebtMarkets the two terms will generally be synonymous: borrowers = issuers.
Investors are buying the promises contained in the new securities. Who are the investors in financial markets? Perhaps the most important class are financial institutions called InvestmentFunds (or simply 'funds') which specialise in investing in securities. For example, a pension fund takes in workers' pension contributions and invests them in securities. In order to reduce the risk from default or devaluation on any particular security, funds will invest across a more or less diverse portfolio of different securities. Other investors may also be issuers - for example, large corporates may invest some of their capital in other institutions' securities as a 'hedge' against particular risks. They might do so directly or through investing in funds.
Financial markets rarely only involve two parties. A bank loan is an example of a two party finance transaction. A corporate goes to a bank and gets money in exchange for a contract promising to make repayments out of future income. The bank invests in the corporate's promise. (Though NB - this is is a finance transaction but not a securities transaction, if the bank cannot then trade on the loan agreement. ?)
More commonly, a security may have only one issuer but it will have a number of investors. And there may also be a number of middlemen - financial institutions employed by the borrower to arrange the deal. These middlemen decide how and where to bring the securities to a public market (PublicOffering); or issue the deal privately by identifying a smaller number of potential investors (PrivatePlacement); work on the paperwork and legal structure of the contract; worry about pricing ...
In a secondary market (see PrimaryAndSecondaryMarkets) the basic types of agents are:
In general, buyers and sellers are all investors adjusting their holdings in the secondary market. (Though in some markets the original issuers may have kept hold of some of their securities, which they can sell at a later date into an existing secondary market.) In general, they should be constantly re-assessing their overall portfolios of securities holdings to increase diversity and maximise their expected profits.
Investors don't actually deal with each other face to face to exchange different securities. Haggling on the 'trading floor' (or nowadays, behind computer screens) is done on their behalf by traders.