It should have been stipulated that unsubscribing should be offered immediately after the option to subscribe.
For instance, if there is a "free trial" period, wait until after that expires, and the customer has been charged, before offering an "unsubscribe".
But aside from the hair-splitting, yes, you are absolutely correct. If I have instant buyer's remorse, I should be able to click it away just as instantly.
"Canceling" a free trial means the trial ends immediately.
"Unsubscribing" during a free trial means the trial continues, but you are no longer subscribed so when the free part of your subscription runs out it won't automatically renew.
I'm not saying your definitions are bad, or wrong... Quite the contrary, I think your ideas are great!
But the specific terms & definitions aren't what really matter, are they? We just need standard language, with specified legal meaning, that consumers can invoke to make service providers jump to task.