usually you're hired by the headhunting firm for a short period, e.g. 6 months, sometimes more or less. you work for the headhunters, your paycheck and insurance is through them, you just work on site / for the other org.
in 6 months if the other org likes you they can hire you on, or if they don't they can just say "get me a new one", etc. in some cases, like you know its a 2 year project, you just stay on for 2 years.
but that means the headhunters are taking 10-30% of what would otherwise be a full-time salary.
