Do Dynatrace (2018 October) updates include updates to the Collectors and Analysis Server ?
If yes, does it work when we install an update using Dynatrace Client in a distributed architecture (Server, Collectors, Analysis Server running on different hosts) ?
For minor version updates these updates get pushed out to all the collected components so being distributed does not matter.
If we're talking about a full version upgrade (e.g. 2018 April to 2018 October) this requires you follow the upgrade guide and does require you to update the collectors and analysis servers manually.
Details on this page.