From the EC-Council's FAQ's:
What is the difference between Exam 312-50 and Exam EC0-350?
EC-Council offers the Certified Ethical Hacker examination over two channels – the EC-Council Accredited Training Center (ATC) and the Authorized Prometric Testing Center (APTC). Only students who undergo training for CEH at any ATC are eligible to appear for the web based Prometric Prime exam (Exam 312-50).
Students who opt to pursue self study can appear for the exam EC0-350 at the Authorized Prometric Testing Center after they fulfill the examination eligibility criteria and produce the voucher number to Prometric.
In all other aspects the exams are identical in source and lead to the certification ‘Certified Ethical Hacker’.
I hope that helps.
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