When Outlook is operating in an Exchange server environment, all rules are stored on the Exchange server (in a hidden folder in the mailbox called Associated Messages). A copy is also retained local to the client in the rwz files as well.
All rules are server-side rules by default (and fire every time a message arrives in the mailbox regardless of whether there is an Outlook session connected to the mailbox or not) except when the rule would require the client to be logged in for the rule to fire correctly - an example of that would be a rule to move a certain message into a client-based PST file, for instance. Because the rule can't fire until the client logs in, the rule is deferred until the client is logged in, and hence is a client-side rule.
So the designation is regarding the environment they fire in, not the storage of the rules.