Is there a minhag difference between tzitzit thickness on the tallit katan?

I was admiring the tzitzit minhag on a guy’s tallit gadol at shul (Yemenite RamBam thick) and asked him about it (at Chabad there’s a bunch of different minhagim!) and briefly mentioned the minhag and that “apparently in Israel thick tzitzit have a different meaning, and I didn’t know that.” And he was pulled away by his family, I guess they were in a rush, so I didn’t get an explanation. The minhag I follow is Sephardi 7-8-11-13 thick on my tallit gadol, but I was always under the impression that it’s a personal matter of choice when it comes to the thickness on the tallit katan. I prefer thick because I teach elementary school and the kids sometimes prank me and tug my tzitzit when I’m not looking. After the thin ones I tried out frayed and broke easily, I’ve just always gone with thick and never thought twice about it. So, is there anything about the thickness of tzitzit on the tallit katan that speaks to a certain minhag? It was never clarified by the guy I talked to what he meant about thickness meaning different things in Israel. Can anyone expound on that?