What does the laa (لا) tajweed symbol mean when reciting the Qur'an?

I was always taught that the laa (لا) symbol meant "Never stop here", and that any recitation would need to continue through it as if it was one phrase. So, for example (taken from the break between [Surah Ya-Sin 79 and 80](https://legacy.quran.com/36/79-80)) As I was taught, this would **always** be recited as **"...`aliimullathii...**", with no break between it. And that if I do catch myself pausing at that point and needing to continue the recitation, I should always back up a few words so I could properly recite the entire thing without pausing, as otherwise I could inadvertently be changing the meaning of the verse into something Islamically unacceptable. However, I have come to be told that there is a difference of opinion regarding this mark in the case of it being above a circle, which I was unaware of. It was definitely not how I was taught, and most English-language resources for reading the Qur'an that I can easily dig up (e.g. https://islam.stackexchange.com/q/4130/22) confirm that it just means "Do not stop, period." and don't mention any difference of opinion in that regard. So the question lies, in the hopes of making this a comprehensive canonical reference, how should the laa (لا) mark be interpreted when reciting the Qur'an? What does it mean, why is it important, and what differences of opinion are there regarding it?