Server-based rules versus client-side rules in M365

Answer

Server-based rules
If you have a M365 account, the server can apply rules to your messages even if Outlook is not running. These are called server-based rules. The rules must be set to be applied to messages when they are delivered to your Inbox on the server, and the rules must be able to run to completion on the server. For example, a rule cannot run to completion on the server if the action specifies that a message be printed. If a rule cannot be applied on the server, it is applied when you start Outlook.

Client-only rules
A "client" is the e-mail program that runs on an individual's computer. A rule that cannot be applied by the server is a "client-only rule" because it runs only on the individual's computer. If your list of rules contains rules that can be run on the server as well as those that cannot, the server-based rules are applied first, followed by the client-only rules.

To create a client-only rule in the Rules Wizard, on the screen for Step 1: Select condition(s), place a check in the option for "on this machine only".