Your business falls under "Third Party" Business. Previously, companies would subcontract for a fixed price for unskilled and other staff. However, many agencies now operate on a service charge percentage basis for monthly outsourcing costs. Despite this, the job still falls under the Contract Labour (Regulation and Abolition) Act, 1970. Even if your liability is limited to salary, PF, and ESI, it is still considered a "Sub-Contract."
Labour licenses are applicable when you deploy 20 or more laborers in a single place under a single agreement. Even if under a single agreement you deploy 20 or more in the same jurisdiction, the Labour Office can require you to obtain a Labour Licence.
One important point is that if the company you are working for is a contractor company (being the prime contractor of the location) and they have a Labour Licence for all deployed labor/staff, you can ask them to issue you a certificate stating "the deployed manpower at the site is included in their Labour Licence." In that case, you will not need to obtain a Labour Licence for that site.
For other registrations, fellow members have already clarified.
Regards