What is the difference between "Equity" and "Private Equity" as an asset class?

As we have the criteria Asset Class (with Equity and Private Equity (under Alternative Investments), Liquidity (Type of Market), and Investment Vehicle the classification goes as follows:

It is Private Equity (under Alternative Investments), when:

The fact that a private equity company is listed on a stock exchange does not influence its core business: investing in unquoted companies.

The phrase “private equity” became widespread in the late 1980s following major buyout fund activity. Private equity, as the term suggests, involves investments of equity capital in private businesses. It provides long-term, committed share capital, to help unquoted companies grow and succeed.

• The underlying investment is privately held, also if it's a single and small company (you can distinguish that in the Investment Vehicle).

• The term private equity does not require that the investing company itself is private. What has been neglected for some time is the existence of listed private equity - an exposure through a share in a private equity company traded on a stock exchange. You can choose accordingly under "Liquidity (Type of Market)" Secondary Market and accordingly the type of how it's traded.

It is an Equity Investment, when:

• The underlying investment is investing in securities, that are usually traded at a stock exchange (secondary market). These securities are usually referred to as stocks or shares.