Round up, like 2-4D is a growth hormone. Basically the plant grows so fast that the cell walls burst and the plant dies.
Gramoxone does not kill the root, only the foliage so weeks later the leaves will be back. Funny story about gramoxone, 30 years ago I worked as part of a lawn maintenance crew. Showed up at one of our clients homes to see dead footprints across the beautifully manicured lawn. One of the guys had sprayed the patio the previous week and instead of starting at the far end and walking backwards he started at the near end, walking over the spray material. the chemical that was on his boots was enough to burn the lawn when he walked back to the truck. Took a few weeks until everything was green again.