A particle system is a dynamically simulated points object. A points object is a type of geometry with points, and very little else. On the other hand, particle systems usually have other properties, like point_velocity and more. Particles are used to simulate things like sparks, fireworks, and fairy dust.
Points objects are also the basis for instances. Instances are copies of geometry like meshes placed at the points' positions. Instances have many uses, such as distributing trees, grass, and rocks on terrain.