The _initial_ implementation of client-side scanning has the same initial result, but vastly different futures. Up until now it could be (foolishly or otherwise) assumed that Apple had your personal privacy in mind. Now they have demonstrated a willingness to compromise your local device privacy. Right now it's iCloud only, but I'm sure it's a boolean configuration away somewhere to make it scan everything, regardless of whether it's marked for iCloud upload or not. And I don't think Apple is strong enough to withstand a gagged demand to flip that boolean.
On their cloud services (Apple, Google, MS, etc) they can only get to content that a user has implicitly agreed to share (whether or not they understand the ramifications is another conversation). On your device, there's no more separation.