In India these two terms are used interchangeably. Frequently the voltage of of electric supply by the power utilities tended to fluctuate much beyond limits suitable for some electrically operated equipments such as refrigerator and TV. Such high fluctuations could cause damage do the equipment in addition to poor performance of the equipment. To over come these problem some companies introduced voltage regulators or stabilizers that drew the power supplied by utilities as input, converted this power to electric current of appropriate voltage irrespective of the voltage on the input side, and fed this as output current for running the appliances.
The word stabilizer implies that output voltage remains same. Similarly the word regulator implies that the output voltage is regulated so that it remains same irrespective of input voltage. Theoretically we can say that a voltage regulator should be capable of regulating voltage to any desired voltage rather than giving just one fixed voltage output. But that is not the way this term is used by common people in India. As this is not use of the term by professionals, it is quite possible that other countries may use this term differently.