How does CurrentControlSet differ from ControlSet001 and ControlSet002?

CurrentControlSet is technically not a "backup" as Gordon states.
It is a symbolic link to one of the ControlSets on the computer. It always points to the ControlSet that is currently loaded.

ControlSet001 may be the last control set you booted with, while ControlSet002 could be what is known as the last known good control set, or the control set that last successfully booted Windows

Yes, you only need to update the CurrentControlSet key...

ControlSet001 and ControlSet002 are alternating backups of CurrentControlSet, you don't need to update them.

Edit: As K noted, CurrentControlSet is an alternating symbolic link to either ControlSet001 or ControlSet002. The other key is kept as a backup for the Load Last Known Good Configuration boot option.

Edit 2: See Microsoft KB Article 100010: What are Control Sets? What is CurrentControlSet?
Original page link broken, see archive.org backup page instead.

Actual symbolic link match is in: HKEY_LOCAL_MACHINE\SYSTEM\Select\.