Sometimes they're interchangeable, but "beam" implies something emitted or directed intentionally, whereas a ray follows its normal optical trajectory. We will also use ray in a poetic context, but not beam. Examples: laser beam (we don't use ray) a beam of light from a flashlight (because we're pointing the flashlight) beam of light (more of a scientific or clinical implication) = ray of light (more metaphoric or literary implication) Her smile was a ray of sunshine on a cloudy day.

Sometimes the words can mean similar things but when talking about light, a beam usually straight and has a narrow focus and goes in a specific direction. The word beam comes from use with physical objects. In construction you might use a beam of wood. Light rays typically spread out or radiate from a central point. The word ray comes from the latin word radius which has more connotations with circles.

In optics, a "ray" is an idealization. it is perfectly thin, perfectly straight line of light. A "beam" is a narrow cone of light. The light is confined to a small angle rather than being allowed to spread in all directions. However, it still has a little spread to it, and mathematically it is made up of an infinite number of rays.