n a binary system, the brighter or more massive object is referred to as primary, and the other the secondary.
Binary stars are also classified based on orbit. Wide binaries are objects with orbits that keep them apart from one another. They evolve separately and have very little effect on each other. Close binaries are close to each other and are able to transfer mass from one another. They can also be classified based on how we observe them. Visual binaries are two stars separated enough that they can be distinguished through binoculars or a small telescope.
Eclipsing binaries are where the objects' orbits are at an angle that when one passes in front of the other it causes an eclipse, as seen from Earth.
Astrometric binaries are objects that seem to move around nothing as their companion object cannot be identified, it can only be inferred. The companion object may not be bright enough or may be hidden in the glare from the primary object.
A related classification though not a binary system is optical binary, which refers to objects that are so close together in the sky that they appear to be a binary system, but are not. Such objects merely appear to be close together, but lie at different distances from the Solar System.[1][2]