Understanding carrier dynamics in photoexcited metal-halide perovskites is key for optoelectronic devices such as solar cells (low carrier densities) and lasers (high carrier densities). Trapping processes at low carrier densities and many-body recombination at high densities can significantly alter the dynamics of photoexcited carriers. Combining optical-pump/THz probe and transient absorption spectroscopy we examine carrier responses over a wide density range (10^14-10^19 cm-3) and temperatures (78-315K) in the prototypical methylammonium lead iodide perovskite. At densities below ~10^15 cm-3 (room temperature, sunlight conditions), fast carrier trapping at shallow trap states occurs within a few picoseconds. As excited carrier densities increase, trapping saturates, and the carrier response stabilizes, lasting up to hundreds of picoseconds at densities around ~10^17 cm-3. Above 10^18 cm-3 a Mott transition sets in: overlapping polaron wavefunctions lead to ultrafast annihilation through an Auger recombination process occurring over a few picoseconds. We map out trap-dominated, direct recombination-dominated, and Mott-dominated density regimes from 78-315 K, ultimately enabling the construction of an electronic phase diagram. These findings clarify carrier behavior across operational conditions, aiding material optimization for optoelectronics operating in the low (e.g. photovoltaics) and high (e.g. laser) carrier density regimes.