The difference between the “update emonpi” and “update emonbase” options via the Admin page of emoncms is only relative to the firmware uploaded to a GPIO attached emonpi or rfm2pi board. The rest of the process and software is identical.
If you do not have an emonpi or rfm2pi (or other serial device) attached to the GPIO, it will make no difference which you use and no benefit in using both. [correction - see the 15th post of Update EmonPi Button or Update EmonBase Button? - #15 by pb66] If you do have a serial device on the GPIO you will need to make your choice carefully as using the wrong one could overwrite your device with incompatible firmware which may not be straightforward to recover from.
[See the Update EmonPi Button or Update EmonBase Button? thread for more info]