An NOC: The NOC giving employer has no objection on your immediate employment within the country however he will not let go the visa with you. Your new employer has to provide you a valid visa to employ you. You'll have to take an exit from the country and return on the new visa. Finger print, medical etc. will follow as if you are a new entrant to Qatar.
A Release: The releasing employer will let you go out to work along with the visa that he obtained in your name. Your new employer does not have to get a visa issued in your name since the same visa can be transferred to the new employer as your new sponsor. You don't need to take an exit. As a convention you also enjoy the right to ask for your visa when you resign or the company wants to terminate your employment for any reason.
Here is the basic difference...
An NOC: The NOC giving employer has no objection on your immediate employment within the country however he will not let go the visa with you. Your new employer has to provide you a valid visa to employ you. You'll have to take an exit from the country and return on the new visa. Finger print, medical etc. will follow as if you are a new entrant to Qatar.
A Release: The releasing employer will let you go out to work along with the visa that he obtained in your name. Your new employer does not have to get a visa issued in your name since the same visa can be transferred to the new employer as your new sponsor. You don't need to take an exit. As a convention you also enjoy the right to ask for your visa when you resign or the company wants to terminate your employment for any reason.