It needs to be turned off at both the host and the clients, recap, but your comment has made me wonder whether the router is responding in some way to the inevitable DHCP requests that will occur while the DHCP Client service is running on one or more clients by switching the DHCP server back on.
Your network card on your client (presumably meaning a PC or laptop) to automatically configure then if your router has DHCP activated then it will issue an IP address that is specified within it's range. IF you are turning DHCP off on your router then no ip addresses will be broadcast and your client will be issued a random meaningless IP address by the O/S.
Check your client IP AFTER you turn DHCP off and if it has an IP within the range of your router 192.168.1.4 for example then DHCP is still on. IF it has an IP of 169.254.68 for example then that is windows generating a random IP and your DHCP is in fact turned off.