In this paper, we prove, for a fairly general class of domains, that the Bergman kernel of a domain is closely related to the normal derivative of the Szegő kernel. Such a result is useful in passing back and forth between estimates for the Bergman projection and estimates for the Szegő projection. We also make some remarks about comparability of the singularity of the Bergman kernel and the singularity of the Szegő kernel.