QAI offers the CSQA, CSQE
ASQ offers the CSQE.

They do overlap some
CSQE has some proj man, testing and quality
CSQA is Processes with some testing
CSQE is testing with some QA.

The web sites will give you body of knowledge listings.

The organizations are independent of each other. So there is no prereq in regards to other certifications to take another. Each does have its own prereqs in order to apply for the exam.

CSQE CSQA had essay in addition to mult choice when I took the exams. This was a few years ago.

CSQE was open book, but you needed to know the material. You would never be able to finish the exam if you looked up everything.