What is the difference between a protostar and a pre-main sequence star?

A protostar is a stage in the formation of a star, when it is still in the process of accumulating matter from its surrounding cloud of gas and dust. At this stage, the temperature and pressure in the core of the protostar are not yet high enough to initiate nuclear fusion reactions, which would produce the energy that powers a star. As the protostar continues to accumulate matter, it becomes denser and its temperature increases until it reaches the point where nuclear fusion can begin. This marks the transition to the next stage in the star's evolution, the pre-main sequence.

A pre-main sequence star is a young star that has just begun nuclear fusion in its core. At this stage, the star is not yet in hydrostatic equilibrium, meaning that the inward force of gravity is still greater than the outward pressure produced by the fusion reactions. This causes the star to contract, which increases its temperature and luminosity until it reaches a point of equilibrium. Once the star has reached this point, it enters the main sequence stage, where it will spend the majority of its life.