PVC sealant

Need info concerning what type sealant required when running PVC pipe from kitchen sink to terracotta pipe drain pipe. Plummers putty will not provide proper sealant

There are rubber adaptors that go from clay to PVC. They can be found at plumbing supply stores, and some of the big box stores. Fernco is one brand.
Is this a sanatary drain or rain water run off?

When joining PVC to PVC, you would use PVC Cement which actually liquifies the surfaces of the pipe and fitting and results in a weld type joint. ABS works the same way using ABS Cement. However, when joining PVC to any other material, you would need to use a no hub or Fernco connector. Which one would depend on if the joint was to be buried or not. The same principal applies to ABS. You match the material and size of the two pipes when selecting the fitting.