Not 100% sure I remember, but I’m pretty sure it’s one of these two (and possibly both).
1) Most likely: Private Equity partnerships typically have multi-year commitments of capital. This means that an investor says: This year I’m giving you $5MM, and I’ll give you another $1.2MM each year for the next 4 years. The understanding is that it takes time to find good PE deals and that the PE manager may not be able to apply the full amount immediately. So Invested Capital would be the money that has already come in, and the committed capital, would be the money that hasn’t come in yet, but which the investor has promised to commit later.
2) Possible: Invested capital may be the money that has already been applied in private equity deals, while committed capital is money that the firm has available to apply to future deals.