Particle systems are used in graphics to represent phenomena like fire, smoke, fog, sparks, splashes, small bits of debris like rocks, splinters, or leaves, as well as magic or sci-fi effects like spells, energy charges, etc. They involve large numbers of lightweight particle entities often rendered as sprites or simple meshes, generated randomly and obeying simple simulation rules, usually without much physics interactions with each other or with the rest of the scene. The primary purpose of particle systems is to create a visual effect as opposed to an accurate simulation, so their appearance and behavior is very much artist-driven.
SPH is a kind of fluid simulation using discrete particle entities to represent parcels of fluid. They are used to estimate the fluid density/pressure/velocity/etc at a given point by averaging over the particles nearby. The advection of fluids is represented by directly moving the particles through space. This is in contrast to the grid-based approach to fluid simulation, where fluid properties are stored at discrete grid points and advection is performed by resampling the grid. There are advantages and disadvantages to both approaches. SPH particles are not usually used directly for rendering; instead, one might use marching cubes or similar to extract an isosurface from a density field defined by the particles, and render that.
There is not much in common between these besides that they use the metaphor of "particles", meaning large numbers of lightweight discrete entities that move around in space according to some rules. One is for a visual effect and is whatever the artist desires, the other is a class of methods for computational fluid dynamics.