The common:

The key differences (not a hard and fast rule):

Venture Capital Private Equity
Philosophy Buying into short-term and high-risk for high-reward Buying to control and sell
Investment model and decision-centricity Invest in the founder’s ability to drive the innovative venture from the point of investment to a big valuation multiple for exit. Invest in a stable, proven business model and profitable company with collateralized assets. Recoup capital through organizational restructuring and financial optimization to achieve scale and exit.
Stake (per financing round) Minority (<20%) Majority (30 - 50 %)
Who runs the company? Founder-led PE-appointed management team
With a controlling stake, most PEs have management decisions to drive the company to their target exit (usually IPO or trade sale)
Valuation approach Revenue multiple Profit multiple