What is the job title of a person who writes and test computer programs?

Answer 1

The person who writes a computer program is called a programmer.

Programmers also typically handle some part of testing, the so-called unit test. Unit testing involves testing a small unit of code in relative isolation, and not necessarily as part of a complete and much larger system.

The person who designs the computer program and its chief principles and algorithms is called a software designer or software architect.

The general term for programmers and architects is software engineer.

The person testing a whole program, within the complete infrastructure, with different operating system versions or user languages, use-cases and whichever other important variation the program is expected to handle, is called a software test engineer or system test engineer.

In larger organizations, one (or more) people are responsible for each of these roles. In smaller organizations, programmer and architect are often the same person, but it is always preferable to have different person design and execute the system testing. In very small organizations, a single person may have to handle all these tasks.

Answer 2

Those are traditionally two separate roles in an organization. The role you are probably thinking of is "X Developer", where X describes a position such as Junior or Senior (describes relative rank to other employees). A developer writes the code and designs automated tests. In the real world, a tester (typically called Quality Assurance or just QA) performs the live testing and provides feedback for the next development iteration.