I did some searches using 擔擔麵 (Dan Dan Mein) and found that there are many variations.
Some are dry; some are in broth.
Some are hot, with chili and sichuan peppercorn; some are not.
Some use tofu; some use minced pork; some use minced pickled vegetable.
Some place the sauce on top of the noodles; some place the sauce under the noodles.
Some contain sesame paste; some don't use sesame paste.
Some serve this hot; some serve this cold (room temperature).
Yet they all use the name 擔擔麵 (Dan Dan Mein).
Yep, that was my understanding as well -- even though this is a dish of origin from Chengdu there is still a lot of regional variation. Sort of like the way Ma Po Tofu is.