I think one of the key distinctions is we do not recognize Hezbollah as representing the Lebanese government.
It is a military parasite that acts independently of the Lebanese people at large.
A cancerous growth that brings death to the Lebanese people, in its crusade to bring death to other people (Israel).
The US Government calls Hezbollah a terrorist group.
The people of Syria also have nothing nice to say after what Hezbollah did for Assad.
Many Syrians, especially the Sunni population, have not forgotten Hezbollah's brutal role in their country's civil war, where it indiscriminately slaughtered their friends and families.