All accelerators are either linear or circular, the difference being whether the particle is shot like a bullet from a gun (the linear accelerator) or whether the particle is twirled in a very fast circle, receiving a bunch of little kicks each time around (the circular accelerator). Both types accelerate particles by pushing them with an electric-field wave.

Linear accelerators (linacs) are used for fixed-target experiments, as injectors to circular accelerators, or as linear colliders.

Fixed target:

Injector to a circular accelerator:

Linear collider:

The beams from a circular accelerator (synchrotron) can be used for colliding-beam experiments or extracted from the ring for fixed-target experiments:

Colliding beams:

Extracted to hit a fixed target:

The particles in a circular accelerator go around in circles because large magnets tweak the particle's path enough to keep it in the accelerator. How do a circular accelerator's magnets make particles go in a circle?