As verbs the difference between threaten and influence
is that
threaten is to make a threat against someone; to use threats while
influence is to affect by gentle action; to exert an influence upon; to modify, bias, or sway; to persuade or induce.
As a noun influence is
the power to affect, control or manipulate something or someone; the ability to change the development of fluctuating things such as conduct, thoughts or decisions.