The Powers That Be
Before I continue, here's my disclaimer - I'm not an expert and claim no absolute definition.
From this and other threads discussing this topic, I've come to the following conclusions. First, the term "Stopping Power" seems to allude to the ability to apply effective ballistic energy to an appropriate area on a target with the end result of immediate termination of aggressive activity.
Second, there are different types of power. Here are a few examples of the differing powers extrapolated from this and other threads.
A .50 BMG round impacting an arm or other appendage may not incapacitate an adversary sufficiently to immediately stop additional aggressive activity. Although, traumatic tissue damage may eventually cause the aggressor to cease all activities. A clear example of "Pausing Power".
A .22 Rimfire impacting COM on a heavily clothed aggressor may have only sufficient ballistic energy to cause a nasty bruise. Such insufficient tissue damage could result in the opposite of the desired result and get the target even more ticked off with the belief that, "Your gun can't hurt me!" An example of "Aggravating Power" My kids can sometimes employ this power without the use of a firearm.
A .38 Special (or any other caliber for that matter) fired into a couch (a miss NOT a warning shot) that causes the aggressor to lose control of their bodily functions and/or to immediately quit the field post haste achieves a similar result to stopping power - the cessation of aggressive behavior. This also has the benefit of no human casualties (although you will have to repair or replace the couch and possibly clean the carpet. This is "Scaring Power".
Often, as evidenced from posts on different threads, "Stopping Power" and "Scaring Power" can occur in conjunction with each other.
Just my humble, if flawed, conclusions from my fallible observations, presented for your entertainment if not worthy of you consideration.