Best Answer - Chosen by the Asker
להפסיק is the closest equivalent to Stop.
לעצור originally means Brake, stop moving, but can often describe the halting of elaborate processes (while להפסיק is attached to immediate actions)
- תפסיק לעבוד על התכנית הזו.
- למה?
- כי החלטנו לעצור את הפרויקט הזה לבינתיים.
לעצור can also be loaned to other contexts to add color or dramatic effect.
i don't think there's a definite answer as they often overlap, and there are some unique scenarios for both, i.e.-
לעצור can also mean "to arrest"
להפסיק is used for quitting a habit (הפסקתי לעשן for example)
as a rule of thumb, if you can use "halt", then use לעצור. otherwise, use להפסיק.
