I learned about this many years ago and the difference after I started using only SLS-free toothpaste was night and day. I used to get canker sores (mouth ulcers) any time I would bite the inside of my cheek, hit my gums with the hard parts of my toothbrush, etc., and this completely stopped a while after I switched to SLS-free.
SLS is Sodium Lauryl Sulfate, by the way, and it’s a detergent. From what I understand, the only reason why it’s added to toothpaste is to make more foam when you brush. But the SLS-free toothpaste I use makes plenty of foam, so I have no idea why they add it. It’s one of those things about the modern world that makes absolutely no sense. The ads and packaging should say in big letters: “now with even more canker sores!”
Unfortunately, the vast majority of toothpastes on the market (at least in the US) have SLS. I can only seem to find SLS-free toothpaste in natural food/supplement stores. It’s extra difficult to find toothpastes that are SLS-free but that keep fluoride too. The difficulty (and price? I haven’t compared) is completely worth it to me though.
TL;DR: The SLS (Sodium Lauryl Sulfate) in most toothpastes is unnecessary and (edit: CAN cause) canker sores (painful sores in your mouth and gums). If you have this problem, you will likely benefit from SLS-free toothpaste (some still include fluoride) that you can usually find at natural food stores.
I used to leave aspirin on the canker, that burned it away.