Private equity is the asset-class identified by limited partners (endowments, pension funds, etc) as an investment allocation in private companies, generally through privately held shares of stock, rather than publicly traded shares. Venture capital is a subcategory of the private equity asset-class, of a unique high-risk/high-yield risk-profile applied to the high-growth trajectory of startup companies.
Generally, private equity will constitute a little above 10% of the total assets under management (AUM) by large money-managers, and venture capital as the subcategory in the single-digit percentages. Hence a reason why the performance of venture capital (up or down) over the years does not tend to make a real dent in the performance of the overall allocation of assets by limited partners. And the real reason why venture capital is allowed to keep playing games with the deployment of subprime innovation arbitrage without serious recourse. But I digress.
The notion that limited partners tuck venture capital in the same asset category as private equity, by the same classes of stock, could not be more misleading. And herein lies my direct answer to your question.
Simply put, private equity is investing after the chasm (Crossing the chasm, By Geoffrey Moore) and venture capital is investing before the chasm. From an innovation perspective, private equity risk-profiles are suitable to support (the commoditization of) downstream innovations and venture capital, if it were to apply a risk-profile of prime innovation, detects and supports the outliers of upstream innovation. In other words, private equity invests in the extrapolation of hindsight and venture capital is supposed to invest in unprecedented foresight.
So, while private equity and venture capital are part of the same asset-allocation bucket of asset/money managers (limited partners), the risk profile of private equity and venture capital are diametrically opposite. Read The State of Venture Capital. The real reason why most limited partners use the wrong criteria to hold the performance of venture capital to account.
Now, because limited partners have confounded the risk-profile with the asset bucket allocation, the risk-profile of venture capital has become steadily (micro)-private equity. Fundamentally incompatible with the nature of the investable asset it was meant to pursue. Hence the reason why entrepreneurs are now forced to obey to risk-averse private-equity innovation arbitrage, unlikely to ever yield upstream evolutionary value.
If you do not grasp any of this asset-management speak, here is an easier way to understand what is going on, using cars as the metaphor in an analogy.
Private equity is a suitcase term akin to cars, which includes a particular vehicle, venture capital, like a Formula-1 version of the car. Today, venture capital performance has been bogged down by criteria by which we make regular cars, in complete ignorance to the unique requirements of a Formula-1 race-car driven on special tracks built for extreme speeds rather than comfort and safety.