Commands that are configured in interface configuration mode override the commands configured using global configuration mode. The ip dhcp-client update dns command (hyphenated) is the global configuration command.
If you specify the both and none keywords in separate configurations, the DHCP client will update both the A and PTR RRs, and the DHCP server will not perform any updates. If you specify the none and both keywords (in this order), the DHCP client will not perform any updates and the server will update both the A and PTR RRs.
There are two parts to the DDNS update configuration on the client side. First, if the ip ddns update method command is configured on the client, which specifies the DDNS-style updates, then the client will be trying to generate or perform A updates. If the ip ddns update method ddns both command is configured, then the client will be trying to update both A and PTR RRs.
Second, the only way for the client to communicate with the server, with reference to what updates it is generating or expecting the server to generate, is to include an FQDN option when communicating with the server. Whether or not this option is included is controlled on the client side by the ip dhcp-client update dns command in global configuration mode or the ip dhcp client update dns command in interface configuration mode.
Even if the client instructs the server to update both or update none, the server can override the client request and do whatever it was configured to do anyway. If there is an FQDN option in the DHCP interaction as above, then the server can communicate to the client that it was overridden, in which case the client will not perform the updates because it knows that the server has done the updates. Even if the server is configured to perform the updates after sending the ACK (the default), it can still use the FQDN option to instruct the client what updates it will be performing and thus the client will not do the same types of updates.
If the server is configured with the update dns command with or without any keywords, and if the server does not see an FQDN option in the DHCP interaction, then it will assume that the client does not understand DDNS and will automatically act as though it were configured to update both A and PTR RRs on behalf of the client.