VC is Private Equity. All thumbs are fingers but not all fingers are thumbs.

My son has lately been claiming that the thumb is not a finger, and he can explain why. I'm not sure who to believe anymore.

Not in the way intended y combinator doesn't do MBO's or dodgy debt loading as far as I know

It sounds like you're conflating asset class (PE) with capital structure (how asset ownership is financed).

Private equity is just an investment of capital in a non-public company in exchange for equity. YC makes capital investments in non-public companies in exchange for equity.

The structure of PE deals can vary from the simple cash investment in exchange for company stock all the way up to incredibly complex leveraged buyouts and everything you could imagine in between.