This means all DNS records registered by the DHCP servers would be owned by the specified account that is common to all DHCP servers.
Those records have an ACL on them to stop registered records from being hijacked by other hosts.
When DHCP is used to allocate IP addresses, the default configuration is shown below—which tells the DHCP server to register records in DNS on behalf of clients only if requested to do so by the client or if the client is unable to dynamically register (e.g., Windows NT 4.0).
When a DHCP server is added to the Dns Update Proxy group, its records aren't secured, meaning that other DHCP servers can update the records.
Dynamic DNS is a feature that allows hosts to register their records in DNS, thus removing the need for administrators to manually create records.
In addition, Secure Dynamic Update can be required for zones that are Active Directory-integrated (and should be required, per best practices), which allows only members of the Authenticated Users group to register records.
This solution is to specify credentials for the DNS dynamic update, which is set on the Advanced tab's IPv4 properties.
You should specify a regular Active Directory user with no special privileges, but the password should be set to never expire (or you should have a really good process to update it periodically! You would then specify this configuration on all DHCP servers so that all DHCP servers use the same account to perform DNS updates.
Q: Does setting DNS dynamic update credentials on DHCP achieve the same result as adding a DHCP server to the Dns Update Proxy group?
A: The short answer is no; however, it's important to step back and understand how DNS interacts with DHCP regarding dynamic updates, then look at what each of the two actions mentioned in the title actually does—namely, setting DNS dynamic update credentials on DHCP and adding a DHCP server to the Dns Update Proxy group.