מחמר

The Meshech Chachma points out that regarding the בני קהת it says זֹ֛את עֲבֹדַ֥ת בְּנֵֽי־קְהָ֖ת בְּאֹ֣הֶל מוֹעֵ֑ד קֹ֖דֶשׁ הַקֳּדָשִֽׁים, but not for בני גרשון ומררי.  Why?  He explains that only the בני קהת actually carried things on their shoulders, they did a real מלאכה but the other families just drove the animals that carried the loads which is only מחמר, not a מלאכה on Shabbos [It is not worthy that they also did מלאכה of carrying the beams from one wagon to another, see Shabbos (96a,) but that wasn't their main job.]
What the M.C. writes that מחמר isn't a מלאכה would seem to be the source of the debate in the opinions cited in Beis Yosef (495:7) if מחמר is prohibited on Yom Tov or not.  If it is a מלאכה, then its prohibited on Yom Tov as well but if its a seperate prohibition, the only source for that is on Shabbos (see also  Gemorah Yevomos 6 and Rashba there.)