During the probation period: "either party may terminate the services with immediate effect without assigning reasons."
Post-probation, i.e., after confirmation of tenure: "Either party will have to terminate services with a notice period of 30 days."
So far as the underlying meanings are concerned, I think you should be clear now. However, though legally the interpretation is correct, office etiquette calls for proper prior intimation of your intentions to be given to the concerned through the proper channel. This will help you in case you would be required to obtain the service/experience certificate, relieving letter, and full and final settlements. Probably this requirement is not mentioned anywhere, I think. Do it sensibly. All the best.
Regards