Every agency I’ve worked with did both. There are short-term, long-term and temp-to-perm jobs, and then there are straight hires. It’s up to you to tell them what you are willing to try.
The employee works for the agency unless and until the company wants to hire them. Until that time, the company pays the agency for the employee, and the agency pays the employee. I always made good money, and some agencies now offer benefits after 90 days. I’ve never been drug tested. Testing was for skills only.
I don’t think you should rule out agencies based on someone else’s limited experience with them.