A traditional employment agency assists job seekers in finding work. Some firms charge the job seeker, so be sure to clarify, upfront, if there is a fee. Others are paid by the employer. In most cases, I would not recommend using an agency that charges the job seeker.
Contingency Employment Agency:
A contingency agency is paid when their candidate is hired by the employer. These types of firms are most often used for low and mid-level searches and they often send a large number of resumes to the employer.
Retained Search Firm:
A retained search firm has an exclusive relationship with the employer. Search firms are typically hired for senior-level searches and for a specific period of time to find a candidate to fill a job. They are paid expenses, plus a percentage of the employee's salary, regardless of whether the candidate is hired.
Temporary (Temp) Agency:
are employment agencies that find employees to fill temporary jobs. For example, temps are often hired to work during seasonal increases in business or to cover vacations or illnesses. Many temporary agencies have expanded their role in the employment sector to fill "temp to perm" positions where they position starts out as a temporary job, but, could become permanent if the employer decides to hire the candidate.