For sysvinit systems chkconfig create a link to the script that run your service from /etc/rc.d/init.d and put it on /etc/rc*.d depending on the run level you specify for your service.
For systemd systems systemctl enable create a link and put it in different folder from the chkconfig in the sysvinit systems.
For example, for multi user level its put it in /etc/systemd/system/multi-user.target.wants/
For you situation if you have a running script in /etc/init.d
So when you call systemd disable it remove the link from /etc/systemd/system/X/
But when you call chkconfig in sysvinit it remove the link from /etc/rc*.d