Release: The employer agrees to let the employee find a new job and "Releases" him/her "with" the visa. Here the new employer doesn't have to apply and obtain a visa for his new employee, only a transfer of sponsorship takes place.

NOC: The employer doesn't "Release" the visa but signs a document (NOC) required to be produced in immigration by the new employer for a visa in his new employee's name. In this case the employee has to take an exit and re-enter Qatar on the new Visa.

Normally releasing is not in the interest of the employer since the same visa can be re-issued in the name of someone he hires and avoid having to apply for a new visa, paying the fee etc. Moreover visas for certain countries are difficult to obtain.
Whereas giving NOC doesn't affect the employer in any way unless he holds some kind of personal grudge against his employee.

Notably the employer is not obliged to give either Release or an NOC to his employee unless some agreement was reached before signing of the contract. :)