What is the difference between Precalculus and Calculus ?
I like the traditional answer. Calculus begins with the introduction of the limit.
There is not one clear statement of what "Precalculus" is. Therefore, I prefer the traditional idea that everything done without limits is pre-calculus.
It may be a course called "Precalculus" or a course called "Algebra 2" or "Functions" or "Advanced Algebra# or some other name.
(I understand that this definition includes non-analytic theory of numbers and many other courses that are -- in the U.S. -- traditionally taught to students after the first 1 or 2 courses in calculus.)
I think that the name "Precalculus" for classes is an attempt to distinguish this course from a course intended for students who will not be taking a calculus class.
I live in northwestern Pennsylvania. This area has many small "tool and die" companies. People who plan careers in this industry need strong skills in algebra, geometry and trigonometry. (And, in the early 21st century, competence with computers is recommended.)
The mathematics required is not trivial. However, students preparing for this career path are not preparing for a calculus course -- as they would, for example, if they were preparing to be the engineers who design the things tool and die makers make.