A thing I've noticed is that my stutter is stronger if I'm "explaining" a meme to someone (lol) - by that I mean that if I saw a meme but I can't show it to another person right now and I'm explaining what it said. I think it is similar to your observation of telling an anecdote or paraphrasing something - my guess is that in these kind of situations, we do not really speak freely - our counterpart knows that we know exactly what we want to say (because anything that is being paraphrased is something where we know its content) and at least to me, I feel like there is a certain expectation from the opposite towards myself (which is rather made up by myself than the other person). in my opinion, this expectation is not as much present if we find ourselves in "normal" conversations where speech is done more freely. In these cases, interrupting speech for a few seconds does not indicate stuttering as much, as it it normal to stop and think about what you are going to say for a moment. To me it's the same reason why I struggle with saying my name fluently (as most people who stutter do) - I feel the need to say it immediately, otherwise people would notice that there's something different / "wrong" with my speech.