Nearly right. The "South Vietnamese" government was an illegal and illegitimate device conjured up by Washington to justify its violent intervention. There was a nation called Vietnam. After international talks, an election was scheduled for Vietnam. Washington decided that the Communists were certain to win the election, so it engineered a "rebellion" by a newly-invented entity called "South Vietnam". Insofar as it ever existed, South Vietnam must have seceded from Vietnam, just as Washington maintains
That's a very good summary.