The only time (that I'm aware of) that you need to install patches at (almost) the same time, is in any sort of a DR / HA setup (clustering, log shipping, etc) You want to keep both SQL Servers at the same version.

Typically with a cluster the recommendation is to move all services to one host, patch and reboot the "inactive" host, once it comes back up and the cluster stabilizes repeat the process for the next host(s).

Otherwise, when and how many servers get patched depends on the business rules and the people doing the patches...