I work at a staffing company that specializes in connecting freelance professionals to organizations and agencies.
According to the contract I signed, I'm a W-2 employee working for them, but will be doing assignments for their clients. So while I'm on their payroll, I don't go to their offices or interact with their employees. My sole interaction is with their clients.
My latest assignment ended last month. While I'm not currently doing any assignments for the staffing company, I'm still employed by them.
I'm currently interviewing for full-time opportunities. In any job application, I'm required to list my current and past employers and provide the dates in which I started and ended work.
I find it hard to explain that my latest job was with company X, although I'm not really hired by X; I'm hired by Y. And while I'm not currently doing any work for Y, the staffing company, I'm still employed by them.
How to explain my situation on paper or during an interview?