The general partner, usually a management entity owned by the fund's principals, makes all investment decisions and receives the management fee and carried-interest. Limited partners have no management role, which is what preserves their limited liability.
Partnerships are generally treated as pass-through entities for tax, so income and gains flow to partners rather than being taxed at the fund level. In the US this produces a schedule-k-1 rather than the simpler forms used for funds.
The partnership agreement is the governing document and it is negotiated, not standard. Key clauses cover fee calculation, the distribution waterfall, key-person provisions, removal rights, and what happens if commitments are not funded. See capital-call.
Related: carried-interest, capital-call, schedule-k-1, private-equity, hedge-fund, master-feeder-structure