The DHCP protocol contains an option where the client can request a remembered IP address from the server (RFC2131, part 3.2).
It seems to me that the difference comes from the DHCP client, whether the allocated address with details is stored in persistent storage which stays over power off or reboot.
Or otherwise, if you can't/don't want to change the dhcp range, to change the addresses to ones outside that range.
But I agree with other posts that assigning fixed addresses by MAC in the router is the more robust way of handling it.
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