Is Complex Analysis the same thing as Complex Variables? What level is this math? College junior math or college senior math? Is it pure or applied math? Is it useful for computer science and electrical engineering majors?

You need to check the course description(s). Courses are named differently in different schools.

Courses also have different degrees of difficulty at different schools. You should go by the course number and how that school numbers the courses.

The probably are the same.

Unless the course description tells you it is referring to one of the other mathematical definitions of the topic.