Le’abed is the effect. Haman needed permission from Achashveirosh to empty out his land. The Gemara talks about those who would have killed us out but didn’t want to be seen as a sliced up kingdom. Achashveirosh wouldn’t really mind having the Jews killed. It is losing subjects that would be the issue.
Le’hashmid means to wipe out. That says all you need to know if you are trying to be specific. When arousing the public he used all descriptions: wipe-out, kill and decimate.