When you change kernels, your nVidia kernel-level driver (nvidia.o) won't load under the new kernel. So once you upgrade to 2.4.18-19.8.0, you'll have to reinstall the drivers (or at least the NVIDIA_kernel package) anyway.
One other thing -- RH 8, AFAIK, doesn't come with kernel 2.4.14. 2.4.14 is quite old (it's actually from before development started on 2.5, which has been going on for quite some time), much older than RH would have normally used. Are you sure this isn't supposed to be kernel 2.4.18-14? Because that is, I believe, the default RH 8 kernel.
Anyway, yes, if you are compiling a new nvidia.o module, you will need a version of kernel-source that corresponds exactly (in both version and configuration) to your running kernel. This means that if you upgrade to 2.4.18-19.8.0, you will need a kernel-source-2.4.18-19.8.0 package installed as well before the nVidia driver will compile. You probably also need to configure that kernel source -- find a config file that matches your architecture in /usr/src/linux-2.4.18-19.8.0/configs, and copy it from there to ../.config. Then cd .., edit the Makefile in there (change EXTRAVERSION from whatever it is to whatever it was minus the "custom" part), and do a make mrproper oldconfig dep to perform the configuration (this takes the settings in the .config file and applies them to the kernel source tree). Then go to wherever you unpacked the NVIDIA_kernel tarball (sometimes the errors from the .tar.gz drivers are better worded than the ones from the .src.rpm), do a make clean, and a make. If you still see errors, post them here.
Oh yeah, do all this while you're running the updated kernel.