Final answer:
A ray is part of a line starting at a point and extending infinitely, while parallel lines are lines in a plane that never intersect.
Step-by-step explanation:
A ray in mathematics refers to part of a line that starts at a point and extends infinitely in one direction. On the other hand, parallel lines are two lines in a plane that do not intersect, no matter how far they are extended in both directions. These definitions are fundamental in the study of geometry, providing a basis for understanding shapes and their properties.