I have my current job through Aerotek. They have more than one type of arrangement between the clients and employees they find.

In my case, the company I work for gave Aerotek info on the qualifications they'd like a prospective employee to have. Then Aerotek searched for candidates. Then the company met with the candidates, and ultimately decided to hire me. In exchange for finding me, the Aerotek was paid a finder's fee that was some percentage of my first year's salary, once I'd held the position for some period of time. That said, I was never an employee of Aerotek, so I was not a contract worker, there was no transition, etc. I've been with this company for 7+ years now, and I earn ~$30,000/year more per year than I did when I started.

If the position the offer is a contract position, they will tell you the details of the contract. When I was hired, I made it clear that I was not interested in a contract position, and they never tried to steer me toward one.