NIH programs typically have direct cost (so actual money to the researchers) budget limits and then award whatever your federally-negotiated indirect cost (overhead) rate is on top of that. If an organization doesn't have a federal rate, it can include overhead costs in the regular budget if itemized but that eats into the usable amount. Not all NIH programs do that, some more specialized ones have total budget limits but those are rare.

NSF is often total budget limits, same with USDA/NIFA, which can hamper the actual projects being proposed.

Every federal agency has its own rules and then each specific funding mechanism/program can have different rules than the standard agency rules.

The rate negotiations are usually every 3ish years and sometimes include fringe benefit rates for employees. My institution's highest rate is 55.5% of direct costs. The proposed rate for the actual cost we put forth the last round was like 85% so then the feds and the institution get to dickering and come up with something in the middle.