A path is geometry, a trajectory is geometry plus time
A path is the purely geometric route a robot follows through space, the sequence of positions or configurations it passes through on its way from start to goal. It says nothing about how fast the robot moves along it or when it reaches any particular point. A trajectory takes that same route and attaches a timestamp to every point on it, specifying not just where the robot goes but exactly when it should be there. This distinction sounds pedantic until you realize it changes what problem you're actually solving.
Consider a robot arm sweeping from one shelf position to another. The path might be a smooth arc through space that avoids a support beam. But that same arc can be executed in two seconds or in twenty. Slower execution means lower velocities and accelerations along the way, faster execution means higher ones. The geometry hasn't changed at all, only the timing has, and yet the physical demands on the robot are completely different.