Seems like it would have the same effect...
Stopping a rule is as close as you can get to uninstalling it without actually doing so: it removes all event subscriptions, scheduled jobs, etc., that might otherwise wake the rule (for example, those your trigger events might otherwise create).
Pausing a rule is less extreme: the rule will still wake in response to trigger event subscriptions but will simply realize that it's paused and not do anything. It also will not do anything to any in-progress actions, such as waits, so a pause and then a resume will put things back how they were before, unlike a stop and start (the latter of which does a full re-initialization like "Install Rule" does the first time or "Done" or "Update Rule" do after).
This is mentioned in the documentation, but if you have any particular concerns, posing a concrete rule example here -- or just trying it yourself, ideally with all logging enabled -- and seeing what the different outcomes are in any particular case you are concerned about is probably the best way to see what the generalizations above mean in your specific use.
So to go one step further... what about using the disable option on a rule? Is it the same thing as stopping the rule?
Good question. And I didn't see it in the docs on quick look.
No, I suppose disabling is a bit more like pausing, except the rule (or any app or driver, really) has no way to know when it's disabled. So, re-enabling won't cause anything to happen on its own. But will entirely stop the app code from running at all in the meantime, per the intent of this feature. It won't technically un-create any subscriptions or schedules, but they also won't mean anything when disabled.
Keep in mind that this is a platform-level feature, not something belonging to any particular app (I think originally intended for things like troubleshooting custom app or driver code that was running away -- there were no stats available at this time -- though technically usable for whatever purpose you consider suitable).
If things were done from new today, it's possible all of these options, plus may others you can use to effectively do the same as some others (e.g., no one has mentioned required expressions as another way to "restrict" rules), wouldn't exist or at least not exist in the same way, but I can't speak to the author on that.
I am only seeing disable and pause. Do not find stop anywhere
Can you share a screenshot of what you do see?
Keep in mind we are talking about Rule Machine, so I'm wondering if you're looking at something else.
I see them on all my rule machine rules, must be getting old and dumber.