I have configured my kernel-2.4.20-8 by using the following commands

make xconfig
make dep
make clean
make bzImage
make modules modules_install
mkinitrd /initrd_new.img 2.4.20-8
cp /usr/src/linux-2.4.20-8/arch/i386/boot/bzImage /boot/new_kernel

OR

cp /boot/vimlinuz-2.4.20-8 /boot/new_kernel
in grub....

title New RedHat
root(hd0,1)
kernel /new-kernel ro root=LABEL=/
initrd /initrd_new.img

.................................................................................................... ...............

Is the new kernel same as the original ?
does it use the same system initilaization files as the original kernel like

init
rc.sysinit
inittab.............and etc etc????

if you did this :
cp /boot/vimlinuz-2.4.20-8 /boot/new_kernel
then you kernel is the very same.

if you did this :
cp /usr/src/linux-2.4.20-8/arch/i386/boot/bzImage /boot/new_kernel
then your kernel is the "new" one, the one you compiled.

of course both use the same system initialisation or config, this is still a linux kernel (and from the same version).

if i want to change the initilaization files for one of the kernel , what should i do? this will effect the other kernel???????

Also i've 2.4.20-8 version of th kernel does this supports graphical boot(process bar screen)?

all kernels "call" the same initialization files, therefore if you change something all kernel will use the change. In fact, most "initialization files" are not relative to the kernel; the first process the kernel start while booting is "init" then init start everything else (so the kernel you are using doesn't matter to your config files). There is no way to change this.

If by "graphical boot" you mean bootsplash feature, then I doubt so, 2.4.20 is quite old ( ~2 years? ), you will need to upgrade to a newer kernel.