Hi mj,
You have to start the main app on each computer, log into your Maxon Account, and then get your update via the main Cinema 4D application update as usual.
The Manual has no entry about an individual Server or Client update function.
(To just copy the whole application folder to each machine is not suggested anywhere. If there is some trouble with this approach, use the clean install above.)
The Registration will be different for R21, no option to just chose Client.
https://www.cineversity.com/vidplaytut/cinema_4d_team_render_part_03
For any technical questions about specific installations, please check with the support team.
Cheers