I’m wondering, what are the white box testers using to create test cases? The actual code? Some kind of diagrams?

I mean, if I am given a task to create test cases for complete branch coverage, is it possible they give me a code?

Because I saw something like that:

Reader r=null;
if(condition)
{
  r=new Reader();
}
r.toString();

There is an obvious bug as the last statement should be in the body of the If statement. It will be easily exposed by false-decision test case of the condition.

But is it not more like unit tests? What is then the white box testers goal of testing?

Wikipedia article on white-box testing states:

The tester chooses inputs to exercise paths through the code and determine the appropriate outputs.

I understand this as you choose inputs to reach the coverage and reveal possible bugs. But isn’t it simple unit testing done by developers?