I never heard any company giving NOC to a newly or fresh employee...just imagine that they hired & spent money to hire you, how can a company give u NOC? You need to finish your contract and NOC will always under company's discretion, you can't force the company to give you.

If you are under probationary period your company won't probably give you NOC.

The difference between the NOC & Release Letter is only the spelling, the meaning is the same, if they give you No Objection Certificate means your company have no objection to release you.